Finite-extensible implies Hall-semidirectly extensible
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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Further information: Finite-extensible automorphism
Hall-semidirectly extensible automorphism
Further information: Hall-semidirectly extensible automorphism
- Finite-semidirectly extensible automorphism is an automorphism that can always be extended from the retract part of a semidirect product.
- Finite-characteristic-semidirectly extensible automorphism is an automorphism that can always be extended from the retract part of a semidirect product, as long as the normal complement is a characteristic subgroup.
This is direct from the definitions.