The average element order and the number of conjugacy classes of finite groups

E. I. Khukhro; A. Moretó; M. Zarrin

The average element order and the number of conjugacy classes of finite groups

Group Theory 2020-09-18 v1

Authors: E. I. Khukhro , A. Moretó , M. Zarrin

Abstract

Let $o(G)$ be the average order of the elements of $G$ , where $G$ is a finite group. We show that there is no polynomial lower bound for $o(G)$ in terms of $o(N)$ , where $N\trianglelefteq G$ , even when $G$ is a prime-power order group and $N$ is abelian. This gives a negative answer to a question of A.~Jaikin-Zapirain.

Keywords

finite groups average element order conjugacy classes polynomial lower bound normal subgroup prime-power order group

Cite

@article{arxiv.2009.08226,
  title  = {The average element order and the number of conjugacy classes of finite groups},
  author = {E. I. Khukhro and A. Moretó and M. Zarrin},
  journal= {arXiv preprint arXiv:2009.08226},
  year   = {2020}
}

The average element order and the number of conjugacy classes of finite groups

Abstract

Keywords

Cite

Related papers