Maximal among abelian normal subgroups

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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 $G$, $H=K$.

Relation with other properties

Weaker properties

• Abelian normal subgroup

Related properties

• Maximal among Abelian characteristic subgroups