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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Item Type:  Article 

Item Status:  Live Archive 
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.
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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