All minimal CL-subgroups have the same derived subgroup

Statement

Suppose $P$ is a group of prime power order. Then, if $A,B$ are two Minimal CL-subgroup (?)s of $P$, the Commutator subgroup (?)s $[A,A]$ and $[B,B]$ are equal.

References

Textbook references

• Corollary 4.2 (Page 490) of Centrally large subgroups of finite p-groups by George Isaac Glauberman, Journal of Algebra, ISSN 00218693, Volume 300,Number 2, Page 480 - 508(Year 2006): ^{Official copyMore info}