University of IsfahanInternational Journal of Group Theory2251-76501420121201CH-groups which are finite $p$-groups923150910.22108/ijgt.2012.1509ENBettinaWilkensLecturer at University of BotswanaJournal Article20120702In their paper "<em>Finite groups whose noncentral commuting elements have centralizers of equal size</em>", S. Dolfi, M. Herzog and E. Jabara classify the groups in question- which they call $ CH$-groups- up to finite $p$-groups. Our goal is to investigate the finite $p$-groups in the class. The chief result is that a finite $p$-group that is a $ CH$-group either has an abelian maximal subgroup or is of class at most $p+1$. Detailed descriptions, in some cases characterisations up to isoclinism, are given.https://ijgt.ui.ac.ir/article_1509_028ff27c245e1f41ebc5c1a1b4f12e07.pdf