Finite-extensible endomorphism

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This article defines a function property, viz a property of functions from a group to itself

Definition

Let G be a finite group and \alpha be an endomorphism of G. We say that \alpha is a finite-extensible endomorphism of G if, for any group H containing G, there exists an endomorphism \alpha' of H such that the restriction of \alpha' to G equals \alpha.

It turns out that any finite-extensible endomorphism must be an automorphism.

Facts