Group property-conditionally extensible automorphism

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This term is related to: extensible automorphisms problem
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Definition

Suppose \alpha is a group property and G is a group satisfying \alpha. An automorphism \sigma of G is termed extensible with respect to \alpha, or extensible conditional to \alpha, if for any group H containing G such that H satisfies property \alpha, there is an automorphism \sigma' of H whose restriction to G equals \sigma.

For more information on the best known results and characterization, refer extensible automorphisms problem.

When the groups satisfying \alpha form a subvariety of the variety of groups, this is equivalent to the notion of variety-extensible automorphism for that subvariety.

Also note that any inner automorphism is conditionally extensible with respect to any group property.

Relation with other properties

Stronger properties

Related properties

Other related notions