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

Khukhro, Evgeny, Moreto, Alexander and Zarrin, Mohammad (2021) The average element order and the number of conjugacy classes of finite groups. Journal of Algebra, 569 . pp. 1-11. ISSN 0021-8693

Full content URL: 10.1016/j.jalgebra.2020.11.009

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The average element order and the number of conjugacy classes of finite groups
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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:$p$-group, nilpotent group, number of conjugacy classes, element orders
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:43085
Deposited On:23 Nov 2020 11:19

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