Abelian normal subgroup of maximum order

Definition
A subgroup $$H$$ of a group of prime power order $$G$$ is termed an abelian normal subgroup of maximum order if it is an abelian normal subgroup (specifically, an abelian normal subgroup of group of prime power order) and there is no abelian normal subgroup of $$G$$ of larger order than $$H$$.

Stronger properties

 * Weaker than::Abelian subgroup of maximum order which is normal

Weaker properties

 * Stronger than::Abelian normal subgroup of group of prime power order
 * Stronger than::Abelian normal subgroup
 * Stronger than::Maximal among abelian normal subgroups