Abelian normal subgroup of group of prime power order

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This article describes a property that arises as the conjunction of a subgroup property: abelian normal subgroup with a group property imposed on the ambient group: group of prime power order
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

Suppose is a group and is a subgroup of . We say that is an abelian normal subgroup of group of prime power order if is an abelian normal subgroup of and is a group of prime power order (i.e., a finite p-group for some prime number ).

Facts

Existence, congruence conditions, and replacement

In the points below, is a prime number.