Extensible local isomorphism

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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 $G$ is a group, $A$ and $B$ are subgroups of $G$ , and $\sigma:A \to B$ is an isomorphism of groups. We say that $σ$ is an extensible local isomorphism if, for any group $K$ containing $G$ , there exists an automorphism $α$ of $K$ such that the restriction of $α$ to $A$ equals $σ$ .

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