# Extensible local isomorphism

This term is related to: Extensible automorphisms problem

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## Definition

Suppose is a group, and are subgroups of , and is an isomorphism of groups. We say that is an **extensible local isomorphism** if, for any group containing , there exists an automorphism of such that the restriction of to equals .

The extensible local isomorphisms conjecture states that an isomorphism of subgroups of is an extensible local isomorphism if and only if it can be extended to an inner automorphism of . This is a strong version of the extensible automorphisms conjecture.