Semipermutable subgroup

A semipermutable subgroup is a concept in the field of group theory, particularly in the study of group extensions and solvable groups. A subgroup \( H \) of a group \( G \) is called **semipermutable** if for every normal subgroup \( N \) of \( G \) such that \( N \) is a subset of \( H \), the subgroup \( H \) permutes with \( N \) in \( G \).