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arXiv · 2206.04339

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

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

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M. Bianchi, R. D. Camina, Mark L. Lewis. 2022-06-09. Conjugacy classes of maximal cyclic subgroups of metacyclic $p$-groups. https://arxiv.org/abs/2206.04339

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