Maximal among abelian normal subgroups

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 $$G$$, $$H = K$$.

Weaker properties

 * Abelian normal subgroup

Related properties

 * Maximal among Abelian characteristic subgroups
 * Self-centralizing subgroup (if inside a supersolvable group):