## 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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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