Group automorphisms

In the context of group theory, an automorphism is an isomorphism from a group to itself. More formally, let \( G \) be a group. An automorphism is a function \( \phi: G \to G \) that satisfies the following properties: 1. **Homomorphism**: For all elements \( a, b \in G \), \( \phi(ab) = \phi(a) \phi(b) \).