Abelian subgroup of maximum order which is normal

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: abelian subgroup of maximum order and abelian normal subgroup of group of prime power order
View other subgroup property conjunctions | view all subgroup properties

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: abelian subgroup of maximum order and abelian normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

Suppose $G$ is a group of prime power order, i.e., $G$ is a finite p-group for some prime number $p$. Suppose $H$ is a subgroup of $G$. We say that $H$ is an abelian subgroup of maximum order which is normal if $H$ is an abelian subgroup of maximum order in $G$ and $H$ is also a normal subgroup of $G$.

Relation with other properties

Weaker properties

• Abelian subgroup of maximum order
• Abelian normal subgroup of group of prime power order, abelian normal subgroup
• Maximal among abelian normal subgroups
• Abelian normal subgroup of maximum order