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416
Table of contents
416
1. Abelian group theory
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Group theory
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1.1. Abelian Lie group
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Abelian group theory
1.2. Abelian group
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Abelian group theory
1.3. Algebraically compact group
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Abelian group theory
1.4. Baer–Specker group
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Abelian group theory
1.5. Basic subgroup
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Abelian group theory
1.6. Butler group
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Abelian group theory
1.7. Cotorsion group
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Abelian group theory
1.8. Cyclic group
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Abelian group theory
1.9. Divisible group
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Abelian group theory
1.10. Elementary abelian group
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Abelian group theory
1.11. Essential subgroup
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Abelian group theory
1.12. Group of rational points on the unit circle
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Abelian group theory
1.13. Height (abelian group)
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Abelian group theory
1.14. Herbrand quotient
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Abelian group theory
1.15. Locally compact abelian group
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Abelian group theory
1.16. Locally cyclic group
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Abelian group theory
1.17. Norm (abelian group)
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Abelian group theory
1.18. Primary cyclic group
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Abelian group theory
1.19. Prüfer group
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Abelian group theory
1.20. Prüfer theorems
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Abelian group theory
1.21. Pure subgroup
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Abelian group theory
1.22. Rank of an abelian group
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Abelian group theory
1.23. Topological abelian group
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Abelian group theory
1.24. Torsion subgroup
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Abelian group theory
2. Algebraic groups
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Group theory
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2.1. Abelian varieties
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Algebraic groups
2.2. Algebraic homogeneous spaces
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Algebraic groups
2.3. E8 (mathematics)
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Algebraic groups
2.4. Exceptional Lie algebras
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Algebraic groups
2.5. Linear algebraic groups
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Algebraic groups
2.6. Representation theory of algebraic groups
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Algebraic groups
2.7. Adelic algebraic group
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Algebraic groups
2.8. Algebraic group
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Algebraic groups
2.9. Approximation in algebraic groups
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Algebraic groups
2.10. Barsotti–Tate group
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Algebraic groups
2.11. Borel subgroup
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Algebraic groups
2.12. Borel–de Siebenthal theory
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Algebraic groups
2.13. Bruhat decomposition
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Algebraic groups
2.14. Cartier duality
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Algebraic groups
2.15. Chevalley's structure theorem
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Algebraic groups
2.16. Cohomological invariant
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Algebraic groups
2.17. Complexification (Lie group)
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Algebraic groups
2.18. Diagonalizable group
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Algebraic groups
2.19. Dieudonné module
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Algebraic groups
2.20. Differential algebraic group
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Algebraic groups
2.21. E6 (mathematics)
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Algebraic groups
2.22. E7 (mathematics)
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Algebraic groups
2.23. F4 (mathematics)
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Algebraic groups
2.24. Fixed-point subgroup
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Algebraic groups
2.25. G2 (mathematics)
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Algebraic groups
2.26. Generalized Jacobian
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Algebraic groups
2.27. Geometric invariant theory
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Algebraic groups
2.28. Jacobson–Morozov theorem
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Algebraic groups
2.29. Kazhdan–Margulis theorem
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Algebraic groups
2.30. Kempf vanishing theorem
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Algebraic groups
2.31. Kneser–Tits conjecture
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Algebraic groups
2.32. Kostant polynomial
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Algebraic groups
2.33. Lang's theorem
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Algebraic groups
2.34. Langlands decomposition
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Algebraic groups
2.35. List of irreducible Tits indices
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Algebraic groups
2.36. Mumford–Tate group
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Algebraic groups
2.37. Pseudo-reductive group
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Algebraic groups
2.38. Radical of an algebraic group
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Algebraic groups
2.39. Restricted Lie algebra
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Algebraic groups
2.40. Root datum
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Algebraic groups
2.41. Rost invariant
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Algebraic groups
2.42. Serre group
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Algebraic groups
2.43. Severi–Brauer variety
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Algebraic groups
2.44. Siegel parabolic subgroup
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Algebraic groups
2.45. Spaltenstein variety
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Algebraic groups
2.46. Tamagawa number
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Algebraic groups
2.47. Taniyama group
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Algebraic groups
2.48. Torus action
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Algebraic groups
2.49. Trace field of a representation
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Algebraic groups
2.50. Verschiebung operator
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Algebraic groups
2.51. Weil's conjecture on Tamagawa numbers
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Algebraic groups
2.52. Weyl module
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Algebraic groups
2.53. Étale group scheme
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Algebraic groups
3. Combinatorial group theory
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Group theory
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3.1. Absolute presentation of a group
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Combinatorial group theory
3.2. Automorphism group of a free group
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Combinatorial group theory
3.3. Baumslag–Solitar group
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Combinatorial group theory
3.4. Commutator collecting process
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Combinatorial group theory
3.5. Freiheitssatz
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Combinatorial group theory
3.6. Fundamental polygon
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Combinatorial group theory
3.7. Hall–Petresco identity
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Combinatorial group theory
3.8. Herzog–Schönheim conjecture
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Combinatorial group theory
3.9. Normal form for free groups and free product of groups
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Combinatorial group theory
3.10. SQ-universal group
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Combinatorial group theory
3.11. Tietze transformations
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Combinatorial group theory
3.12. Von Neumann conjecture
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Combinatorial group theory
4. Coxeter groups
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Group theory
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4.1. Bruhat order
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Coxeter groups
4.2. Coxeter element
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Coxeter groups
4.3. Coxeter group
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Coxeter groups
4.4. Coxeter–Dynkin diagram
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Coxeter groups
4.5. Longest element of a Coxeter group
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Coxeter groups
4.6. Reflection group
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Coxeter groups
5. Functional subgroups
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Group theory
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5.1. Fitting subgroup
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Functional subgroups
6. Group automorphisms
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Group theory
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6.1. Automorphism group
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Group automorphisms
6.2. Quotientable automorphism
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Group automorphisms
7. Group products
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Group theory
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7.1. Direct product of groups
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Group products
7.2. Product of group subsets
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Group products
7.3. Semidirect product
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Group products
8. Infinite group theory
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Group theory
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8.1. Commensurability (group theory)
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Infinite group theory
8.2. Elementary amenable group
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Infinite group theory
8.3. FC-group
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Infinite group theory
8.4. Free-by-cyclic group
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Infinite group theory
8.5. Gromov's theorem on groups of polynomial growth
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Infinite group theory
8.6. Higman's embedding theorem
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Infinite group theory
8.7. Hopfian group
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Infinite group theory
8.8. Infinite dihedral group
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Infinite group theory
8.9. Infinite group
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Infinite group theory
8.10. Locally finite group
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Infinite group theory
8.11. Pro-p group
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Infinite group theory
8.12. Profinite group
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Infinite group theory
8.13. Prüfer rank
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Infinite group theory
8.14. Residually finite group
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Infinite group theory
8.15. Residue-class-wise affine group
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Infinite group theory
8.16. Tarski monster group
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Infinite group theory
8.17. Thompson groups
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Infinite group theory
8.18. Tits alternative
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Infinite group theory
8.19. Verbal subgroup
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Infinite group theory
8.20. Z-group
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Infinite group theory
9. Moonshine theory
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Group theory
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9.1. Kac–Moody algebra
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Moonshine theory
9.2. Monster Lie algebra
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Moonshine theory
9.3. Monster group
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Moonshine theory
9.4. Supersingular prime (moonshine theory)
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Moonshine theory
10. Ordered groups
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Group theory
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10.1. Archimedean group
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Ordered groups
10.2. Cyclically ordered group
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Ordered groups
10.3. Hahn embedding theorem
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Ordered groups
10.4. Linearly ordered group
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Ordered groups
10.5. Ordered field
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Ordered groups
10.6. Ordered ring
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Ordered groups
10.7. Partially ordered group
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Ordered groups
10.8. Riesz space
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Ordered groups
11. P-groups
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Group theory
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11.1. Coclass
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P-groups
11.2. Extra special group
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P-groups
11.3. Focal subgroup theorem
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P-groups
11.4. P-group
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P-groups
11.5. Powerful p-group
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P-groups
11.6. Regular p-group
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P-groups
11.7. Special group (finite group theory)
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P-groups
11.8. Sylow theorems
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P-groups
12. Representation theory of groups
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Group theory
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12.1. Representation theory of Lie groups
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Representation theory of groups
12.2. Representation theory of finite groups
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Representation theory of groups
12.3. Unitary representation theory
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Representation theory of groups
12.4. Atlas of Lie groups and representations
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Representation theory of groups
12.5. B-admissible representation
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Representation theory of groups
12.6. Character theory
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Representation theory of groups
12.7. Complex conjugate representation
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Representation theory of groups
12.8. Complex representation
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Representation theory of groups
12.9. Corepresentations of unitary and antiunitary groups
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Representation theory of groups
12.10. Dual representation
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Representation theory of groups
12.11. Fontaine's period rings
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Representation theory of groups
12.12. Frobenius–Schur indicator
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Representation theory of groups
12.13. Gelfand pair
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Representation theory of groups
12.14. Gelfand–Raikov theorem
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Representation theory of groups
12.15. Group ring
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Representation theory of groups
12.16. K-finite
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Representation theory of groups
12.17. Matrix coefficient
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Representation theory of groups
12.18. McKay conjecture
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Representation theory of groups
12.19. Molien's formula
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Representation theory of groups
12.20. Multiplicity-one theorem
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Representation theory of groups
12.21. P-adic Hodge theory
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Representation theory of groups
12.22. Partial group algebra
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Representation theory of groups
12.23. Regular representation
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Representation theory of groups
12.24. Representation rigid group
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Representation theory of groups
12.25. Representation theory of diffeomorphism groups
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Representation theory of groups
12.26. Schur orthogonality relations
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Representation theory of groups
12.27. Schur–Weyl duality
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Representation theory of groups
12.28. Springer correspondence
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Representation theory of groups
12.29. Tempered representation
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Representation theory of groups
13. Subgroup properties
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Group theory
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13.1. Abnormal subgroup
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Subgroup properties
13.2. Ascendant subgroup
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Subgroup properties
13.3. C-normal subgroup
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Subgroup properties
13.4. Carter subgroup
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Subgroup properties
13.5. Central subgroup
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Subgroup properties
13.6. Centrally closed subgroup
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Subgroup properties
13.7. Characteristic subgroup
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Subgroup properties
13.8. Conjugate-permutable subgroup
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Subgroup properties
13.9. Contranormal subgroup
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Subgroup properties
13.10. Descendant subgroup
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Subgroup properties
13.11. Fully normalized subgroup
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Subgroup properties
13.12. Hall subgroup
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Subgroup properties
13.13. Malnormal subgroup
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Subgroup properties
13.14. Maximal subgroup
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Subgroup properties
13.15. Modular subgroup
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Subgroup properties
13.16. Normal subgroup
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Subgroup properties
13.17. Paranormal subgroup
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Subgroup properties
13.18. Polynormal subgroup
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Subgroup properties
13.19. Pronormal subgroup
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Subgroup properties
13.20. Quasinormal subgroup
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Subgroup properties
13.21. Seminormal subgroup
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Subgroup properties
13.22. Semipermutable subgroup
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Subgroup properties
13.23. Serial subgroup
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Subgroup properties
13.24. Special abelian subgroup
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Subgroup properties
13.25. Subnormal subgroup
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Subgroup properties
13.26. Transitively normal subgroup
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Subgroup properties
14. Subgroup series
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Group theory
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14.1. Central series
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Subgroup series
14.2. Chief series
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Subgroup series
14.3. Fitting length
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Subgroup series
15. Topological groups
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Group theory
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15.1. Discrete groups
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Topological groups
15.2. Amenable group
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Topological groups
15.3. Bohr compactification
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Topological groups
15.4. Cantor cube
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Topological groups
15.5. Chabauty topology
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Topological groups
15.6. Compact group
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Topological groups
15.7. Compactly generated group
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Topological groups
15.8. Continuous group action
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Topological groups
15.9. Covering group
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Topological groups
15.10. Direct sum of topological groups
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Topological groups
15.11. Discontinuous group
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Topological groups
15.12. Extension of a topological group
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Topological groups
15.13. Haar measure
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Topological groups
15.14. Hilbert–Smith conjecture
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Topological groups
15.15. Homogeneous space
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Topological groups
15.16. Identity component
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Topological groups
15.17. Kazhdan's property (T)
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Topological groups
15.18. Kronecker's theorem
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Topological groups
15.19. Locally compact group
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Topological groups
15.20. Locally profinite group
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Topological groups
15.21. Loop group
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Topological groups
15.22. Maximal compact subgroup
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Topological groups
15.23. Monothetic group
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Topological groups
15.24. One-parameter group
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Topological groups
15.25. Paratopological group
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Topological groups
15.26. Peter–Weyl theorem
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Topological groups
15.27. Positive real numbers
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Topological groups
15.28. Quasiregular representation
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Topological groups
15.29. Restricted product
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Topological groups
15.30. Schwartz–Bruhat function
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Topological groups
15.31. Semitopological group
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Topological groups
15.32. Topological group
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Topological groups
15.33. Topological ring
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Topological groups
15.34. Totally disconnected group
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Topological groups
16. (B, N) pair
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Group theory
17. Acylindrically hyperbolic group
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Group theory
18. Affine group
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Group theory
19. Approximate group
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Group theory
20. Artin transfer (group theory)
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Group theory
21. Baby-step giant-step
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Group theory
22. Banach–Tarski paradox
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Group theory
23. Bass–Serre theory
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Group theory
24. Bender's method
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Group theory
25. Bianchi group
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Group theory
26. Bicommutant
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Group theory
27. Bimonster group
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Group theory
28. Bol loop
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Group theory
29. Burnside problem
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Group theory
30. CN-group
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Group theory
31. Caesar cipher
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Group theory
32. Center (group theory)
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Group theory
33. Character group
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Group theory
34. Character table
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Group theory
35. Class automorphism
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Group theory
36. Class function
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Group theory
37. Cohomological dimension
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Group theory
38. Commutator subgroup
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Group theory
39. Complement (group theory)
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Group theory
40. Complex reflection group
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Group theory
41. Component (group theory)
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Group theory
42. Conjugacy class
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Group theory
43. Conjugacy class sum
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Group theory
44. Conjugacy problem
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Group theory
45. Conjugation of isometries in Euclidean space
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Group theory
46. Core (group theory)
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Group theory
47. Coset
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Group theory
48. Cremona group
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Group theory
49. De Sitter invariant special relativity
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Group theory
50. Dedekind group
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Group theory
51. Demushkin group
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Group theory
52. Descendant tree (group theory)
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Group theory
53. Diagonal subgroup
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Group theory
54. Direct sum of groups
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Group theory
55. Double coset
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Group theory
56. Double group
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Group theory
57. Ehlers group
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Group theory
58. Elliptic curve
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Group theory
59. Embedding problem
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Group theory
60. Engel group
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Group theory
61. Engel identity
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Group theory
62. Examples of groups
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Group theory
63. Fibonacci group
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Group theory
64. Finitely generated group
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Group theory
65. Finiteness properties of groups
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Group theory
66. Fixed points of isometry groups in Euclidean space
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Group theory
67. Formation (group theory)
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Group theory
68. Frattini subgroup
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Group theory
69. G-module
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Group theory
70. Generalized dihedral group
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Group theory
71. Generating set of a group
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Group theory
72. Geometric group theory
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Group theory
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72.1. (2,3,7) triangle group
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Geometric group theory
72.2. Adian–Rabin theorem
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Geometric group theory
72.3. Asymptotic dimension
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Geometric group theory
72.4. Curve complex
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Geometric group theory
72.5. Discrete group
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Geometric group theory
72.6. Flexagon
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Geometric group theory
72.7. Free factor complex
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Geometric group theory
72.8. Fully irreducible automorphism
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Geometric group theory
72.9. Følner sequence
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Geometric group theory
72.10. Geometric group action
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Geometric group theory
72.11. Graph of groups
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Geometric group theory
72.12. Gromov boundary
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Geometric group theory
72.13. Grushko theorem
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Geometric group theory
72.14. Haagerup property
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Geometric group theory
72.15. Kurosh subgroup theorem
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Geometric group theory
72.16. Mapping class group of a surface
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Geometric group theory
72.17. Out(Fn)
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Geometric group theory
72.18. Outer space (mathematics)
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Geometric group theory
72.19. Quasi-isometry
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Geometric group theory
72.20. Relatively hyperbolic group
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Geometric group theory
72.21. Rips machine
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Geometric group theory
72.22. Stallings theorem about ends of groups
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Geometric group theory
72.23. Subgroup distortion
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Geometric group theory
72.24. Thurston boundary
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Geometric group theory
72.25. Ultralimit
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Geometric group theory
72.26. Weyl distance function
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Geometric group theory
72.27. Švarc–Milnor lemma
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Geometric group theory
73. Glossary of group theory
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Group theory
74. Grigorchuk group
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Group theory
75. Group extension
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Group theory
76. Group of Lie type
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Group theory
77. Group representation
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Group theory
78. Group structure and the axiom of choice
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Group theory
79. Hall's identity
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Group theory
80. Hanna Neumann conjecture
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Group theory
81. Higman group
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Group theory
82. Higman–Sims asymptotic formula
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Group theory
83. History of group theory
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Group theory
84. Holomorph (mathematics)
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Group theory
85. Homeomorphism group
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Group theory
86. IA automorphism
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Group theory
87. Idempotent measure
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Group theory
88. Index calculus algorithm
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Group theory
89. Index of a subgroup
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Group theory
90. Induced character
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Group theory
91. Induced representation
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Group theory
92. Inner automorphism
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Group theory
93. Invariant decomposition
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Group theory
94. Lattice of subgroups
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Group theory
95. Leinster group
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Group theory
96. Length function
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Group theory
97. List of character tables for chemically important 3D point groups
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Group theory
98. List of finite simple groups
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Group theory
99. List of group theory topics
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Group theory
100. Lorentz group
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Group theory
101. Lyndon–Hochschild–Serre spectral sequence
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Group theory
102. Magnetic space group
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Group theory
103. Maria Wonenburger
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Group theory
104. Measurable acting group
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Group theory
105. Measurable group
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Group theory
106. Mennicke symbol
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Group theory
107. Modular group
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Group theory
108. Moufang loop
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109. Moufang set
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110. Multiplicative character
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111. No small subgroup
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112. Norm (group)
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113. Normal closure (group theory)
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114. Nottingham group
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115. Opposite group
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116. Outer automorphism group
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117. P-group generation algorithm
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118. Perfect core
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119. Picard modular group
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120. Point group
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121. Point groups in three dimensions
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122. Point groups in two dimensions
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123. Power automorphism
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124. Power closed
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125. Principal homogeneous space
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126. Principal ideal theorem
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127. Principalization (algebra)
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128. Projective representation
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129. Quasigroup
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130. Quasimorphism
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131. Quasirandom group
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132. Quaternion group
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133. Quotient group
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134. Rank of a group
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135. Real element
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136. Real tree
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137. Representation on coordinate rings
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138. Representation ring
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139. Resolvent (Galois theory)
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140. Retract (group theory)
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141. SL2(R)
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142. Schoof's algorithm
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143. Schoof–Elkies–Atkin algorithm
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144. Schottky group
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145. Schur multiplier
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146. Spherical 3-manifold
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147. Subgroup
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148. Subgroup method
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149. Suzuki group
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150. Symmetric set
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151. Transfer (group theory)
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152. Virtually
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153. Von Neumann paradox
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154. Whitehead problem
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155. Wyckoff positions
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156. Zappa–Szép product
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Group theory
Ancestors
Fields of abstract algebra
Fields of mathematics
Mathematics
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