CH-groups which are finite $p$-groups

Abstract

In 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.