Fixed-class extensible automorphism

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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.

Relation with other properties

Weaker properties