On the average order of a finite group

DOI10.1016/J.JPAA.2022.107276arXiv2210.16666MaRDI QIDQ6415499

Marius Tărnăuceanu, Mihai-Silviu Lazorec

Publication date: 29 October 2022

Abstract: Let $o(G)$ be the average order of a finite group $G$. We show that if $o(G)<c$, where $cinlbracefrac136,frac114brace$, then $G$ is an elementary abelian 2-group or a solvable group, respectively. Also, we prove that the set containing the average orders of all finite groups is not dense in $[a,infty)$, for all $ain[0,frac136]$. We also outline some results related to the integer values of the average order. Since group element orders is a popular research topic, we pose some open problems concerning the average order of a finite group throughout the paper.

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Finite nilpotent groups, (p)-groups (20D15)

This page was built for publication: On the average order of a finite group

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6415499)