Maximal among Abelian normal subgroups

From Groupprops

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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.
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RANDOM SUBGROUP PROPERTY: Abelian normal subgroup: A subgroup that is Abelian as a group and normal as a subgroup.

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 all properties obtained by applying the maximal operator