Finite-extensible implies Hall-semidirectly extensible

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This article gives the statement and possibly, proof, of an implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property (i.e., finite-extensible automorphism) must also satisfy the second automorphism property (i.e., Hall-semidirectly extensible automorphism)
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Suppose G is a finite group and \sigma is a finite-extensible automorphism of G. Then, \sigma is a Hall-semidirectly extensible automorphism of G.

Definitions used

Finite-extensible automorphism

Further information: Finite-extensible automorphism

Hall-semidirectly extensible automorphism

Further information: Hall-semidirectly extensible automorphism

Related facts

Intermediate properties


This is direct from the definitions.