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. 111.
ISSN 00218693
Full content URL: 10.1016/j.jalgebra.2020.11.009
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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 primepower order group and $N$ is abelian. This gives a negative answer to a question of A. JaikinZapirain.
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