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arXiv · 2009.08226

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

E. I. Khukhro·A. Moretó·M. Zarrin
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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.

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E. I. Khukhro, A. Moretó, M. Zarrin. 2020-09-17. The average element order and the number of conjugacy classes of finite groups. https://arxiv.org/abs/2009.08226

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