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CH-groups which are finite p-groups

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

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Abstract:

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+1. Detailed descriptions,in some cases characterisations up to isoclinism, are given.

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