Characterizing some finite groups by the average order
Group Theory
2023-07-31 v1
Abstract
The average order of a finite group G is denoted by o(G). In this note, we classify groups whose average orders are less than o(S4), where S4 is the symmetric group on four elements. Moreover, we prove that G \cong S4 if and only if o(G) = o(S4). As a consequence of our results we give a characterization for some finite groups by the average order. In [9, Theorem 1.2], the groups whose average orders are less than o(A4) are classified. It is worth mentioning that to get our results we avoid using the main theorems of [9] and our results leads to reprove those theorems.
Keywords
Cite
@article{arxiv.2307.15328,
title = {Characterizing some finite groups by the average order},
author = {Ashkan Zarezadeh and Behrooz Khosravi and Zeinab Akhlaghi},
journal= {arXiv preprint arXiv:2307.15328},
year = {2023}
}