Kernel of a characteristic action on an abelian group
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]
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A subgroup of a group is termed a kernel of a characteristic action on an abelian group if there exists an abelian group and a homomorphism with kernel , such that is a characteristic subgroup of the semidirect product .
Relation with other properties
- Normal subgroup of finite group
- Normal subgroup of a group having no nontrivial abelian normal -subgroup for some prime .