Hall-semidirectly extensible automorphism

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This term is related to: Extensible automorphisms problem
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Definition

Let G be a finite group and \sigma be an automorphism of G. \sigma is termed Hall-semidirectly extensible if for every group K containing <mah>G</math> as a Hall retract, i.e., containing G as a Hall subgroup with a normal complement, there exists an automorphism \sigma' of K whose restriction to G is \sigma.

Relation with other properties

Stronger properties

Weaker properties