Conjugacy classes of maximal cyclic subgroups and nilpotence class of $p$-groups

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

Conjugacy classes of maximal cyclic subgroups and nilpotence class of $p$-groups

Group Theory 2022-01-19 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 $G$ . We prove that if $G$ is a $p$ -group of order $p^n$ and nilpotence class $l$ , then $\eta (G)$ is bounded below by a linear function in $n/l$ .

Keywords

p-groups conjugacy classes maximal cyclic subgroups nilpotence class group order

Cite

@article{arxiv.2201.05642,
  title  = {Conjugacy classes of maximal cyclic subgroups and nilpotence class of $p$-groups},
  author = {M. Bianchi and R. D. Camina and Mark L. Lewis},
  journal= {arXiv preprint arXiv:2201.05642},
  year   = {2022}
}

Comments

9 pages

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