The conjugacy classes and commuting degree of the  -groups with a cyclic subgroup of index

The conjugacy classes and commuting degree of the $p$ -groups with a cyclic subgroup of index $p^2$

Mohammad Naghshinehfard

Abstract

We compute the number of conjugacy classes in $p$ -groups of order $p^n$ and exponent $p^{n-2}$ classified by Ninomiya in $1994$ . This enables us to obtain the commuting degrees of these groups.

Keywords: Commuting degree; conjugacy class; p-group

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The conjugacy classes and commuting degree of the -groups with a cyclic subgroup of index

Abstract

The conjugacy classes and commuting degree of the $p$ -groups with a cyclic subgroup of index $p^2$