Maximal among abelian normal subgroups

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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]

Definition

Symbol-free definition

A subgroup of a group is termed maximal among Abelian normal subgroups if it is an Abelian normal subgroup and there is no Abelian normal subgroup properly containing it.

Definition with symbols

A subgroup H of a group G is termed maximal among Abelian normal subgroups if H is an Abelian normal subgroup of G, and for any K containing H that is an Abelian normal subgroup of G, H = K.

Formalisms

In terms of the maximal operator

This property is obtained by applying the maximal operator to the property: Abelian normal subgroup
View other properties obtained by applying the maximal operator

Relation with other properties

Weaker properties

Related properties