CH-groups which are finite p-groups

In their paper "Finite groups whose noncentral commuting elements have centralizers of equal size"‎, ‎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+۱‎. ‎Detailed descriptions‎, ‎in some cases characterisations up to isoclinism‎, ‎are given‎.

Keywords:

Finite-p-groups , AC-groups , conjugate rank