Minimal CL-subgroup

Definition
Let $$P$$ be a group of prime power order. A subgroup $$A$$ of $$P$$ is termed a minimal CL-subgroup or minimal centrally large subgroup of $$P$$ if $$A$$ is a defining ingredient::centrally large subgroup of $$P$$ and no proper subgroup of $$A$$ is a centrally large subgroup of $$P$$.

Weaker properties

 * Stronger than::Centrally large subgroup

Facts

 * All minimal CL-subgroups have the same commutator subgroup