Center of critical subgroup

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

Stronger properties

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

Weaker properties

 * Stronger than::Abelian characteristic subgroup
 * Stronger than::Subgroup containing the center