Conjugacy classes of maximal cyclic subgroups of metacyclic $p$-groups

M. Bianchi; R. D. Camina; Mark L. Lewis

Conjugacy classes of maximal cyclic subgroups of metacyclic $p$-groups

Group Theory 2022-06-10 v1

Authors: M. Bianchi , R. D. Camina , Mark L. Lewis

Abstract

In this paper, we set $\eta (G)$ to be the number of conjugacy classes of maximal cyclic subgroups of a finite group $G$ . We compute $\eta (G)$ for all metacyclic $p$ -groups. We show that if $G$ is a metacyclic $p$ -group of order $p^n$ that is not dihedral, generalized quaternion, or semi-dihedral, then $\eta (G) \ge n-2$ , and we determine when equality holds.

Cite

@article{arxiv.2206.04339,
  title  = {Conjugacy classes of maximal cyclic subgroups of metacyclic $p$-groups},
  author = {M. Bianchi and R. D. Camina and Mark L. Lewis},
  journal= {arXiv preprint arXiv:2206.04339},
  year   = {2022}
}

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