Open main menu

Groupprops β

Kernel of a characteristic action on an abelian group

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