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 with symbols

Let \sigma be an automorphism of a group G. Then \sigma is said to be semidirectly extensible if the following holds. For any homomorphism \rho:G \to Aut(N) for a group N, consider the semidirect product M = N \rtimes G. Then, there exists an automorphism \varphi of M that leaves both N and G invariant, and whose restriction to G is \sigma.

Relation with other properties

Weaker properties