Perfect normal subgroup

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This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): perfect group
View a complete list of such conjunctions
This article describes a property that arises as the conjunction of a subgroup property: permutable subgroup with a group property (itself viewed as a subgroup property): perfect group
View a complete list of such conjunctions

Definition

Symbol-free definition

A subgroup of a group is termed a perfect normal subgroup if it satisfies the following equivalent conditions:

Definition with symbols

A subgroup H of a group G is termed a perfect normal subgroup if [H,H] = [G,H] = H.

Relation with other properties

Stronger properties

Weaker properties