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