# Extensible endomorphism

From Groupprops

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Template:Endomorphism propertyBEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

Let be a group and be an endomorphism of . We say that is **extensible** if, for any group containing , there is an endomorphism of such that the restriction of to equals .

## Related terms

An extensible automorphism is an automorphism that can always be extended to an automorphism for any bigger group. Every extensible automorphism is an extensible endomorphism and also an automorphism. However, there is no *a priori* reason that every extensible endomorphism that is also an automorphism should be an extensible automorphism.

A finite-extensible endomorphism is an endomorphism of a finite group that can always be extended to an endomorphism for any finite group containing it.