On the Conjugacy Classes of Cyclic Non-normal Subgroups

Abstract

Let G be a finite p-group. Assume that \(\nu (G)\) and \(\nu _c(G)\) denote the number of conjugacy classes of non-normal subgroups and non-normal cyclic subgroups of G, respectively. In this paper, we completely classify the finite p-groups with \(\nu _c=p\) or \(p+1\) for an odd prime number p. Also, we classify the groups G with \(\nu (G)=\nu _c(G)=p^i, i\ge 1\).

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Correspondence to Hamid Mousavi.

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Communicated by Mohammad Zarrin.

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Mousavi, H. On the Conjugacy Classes of Cyclic Non-normal Subgroups. Bull. Iran. Math. Soc. (2021). https://doi.org/10.1007/s41980-020-00502-6

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Keywords

  • Non-normal subgroups
  • Conjugacy class of non-normal subgroups

Mathematics Subject Classification

  • 20E45
  • 20D25