Kernel of a characteristic action on an abelian group

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

A subgroup H of a group G is termed a kernel of a characteristic action on an abelian group if there exists an abelian group V and a homomorphism \alpha:G \to \operatorname{Aut}(V) with kernel H, such that V is a characteristic subgroup of the semidirect product V \rtimes G.

Relation with other properties

Stronger properties

Weaker properties