# Hall-semidirectly extensible automorphism

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This term is related to: Extensible automorphisms problem

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## Definition

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