# Fixed-class extensible automorphism

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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This is the property of being a variety-extensible automorphism for the following variety of algebras: fixed-class nilpotent groups

## Definition

### Definition with symbols

Let $G$ be a nilpotent group and let $c$ be the nilpotence class of $G$. An automorphism $\sigma$ of $G$ is said to be fixed-class extensible if, for any embedding $G \le H$ in a group $H$ of nilpotence class $c$, there exists an automorphism $\sigma'$ of $H$ such that the restriction of $\sigma'$ to $G$ is $\sigma$.