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 \( a, b \in G \), \( \phi(ab) = \phi(a) \phi(b) \).

In mathematics, specifically in the field of group theory and abstract algebra, an automorphism group is a concept that involves the symmetries of a mathematical structure. ### Definition An **automorphism** is an isomorphism from a mathematical object to itself. In other words, it is a bijective mapping that preserves the structure of the object.

In the context of mathematics, particularly in group theory and the study of algebraic structures, the term "quotientable automorphism" is not a standard terminology widely recognized in classic mathematical literature. However, I can help clarify two concepts that might relate to this phrase: 1. **Automorphism**: An automorphism is a structure-preserving map from a mathematical object to itself that has an inverse.