Group property-conditionally extensible automorphism
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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 α is a group property and G is a group satisfying α. An automorphism σ of G is termed extensible with respect to α, or extensible conditional to α, if for any group H containing G such that H satisfies property α, there is an automorphism σ' of H whose restriction to G equals σ.
For more information on the best known results and characterization, refer extensible automorphisms problem.
When the groups satisfying α 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.
