Center of critical subgroup

Definition

Suppose $P$ is a group of prime power order. A subgroup $K$ of $P$ is termed a center of critical subgroup of $P$ if there exists a critical subgroup $C$ of $G$ such that $Z(C)=K$.

Relation with other properties

Stronger properties

• Maximal among Abelian characteristic subgroups (for a group of prime power order)

Weaker properties

• Abelian characteristic subgroup
• Subgroup containing the center