# Extensible local isomorphism

From Groupprops

This term is related to: Extensible automorphisms problem

View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem

## 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.