Potentially characteristic-semidirectly extensible automorphism

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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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This is a variation of extensible automorphism|Find other variations of extensible automorphism |
This term is related to: Extensible automorphisms problem
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Definition

Definition with symbols

Let \sigma be an automorphism of a group G. Then \sigma is said to be potentially characteristic-semidirectly extensible if the following holds:

Let \rho:G \to Aut(N) be a homomorphism such that N is a potentially characteristic subgroup of the semidirect product M of N with G. Then, there exists an automorphism \phi of M that leaves both N and G invariant, and whose restriction to G is \sigma.

Relation with other properties

Stronger properties

Weaker properties