Another criterion for solvability of finite groups
Group Theory
2021-12-09 v1
Abstract
Let G be a finite group. Denote by \psi(G) the sum \psi(G)=\sum_{x\in G}|x| where |x| denotes the order of the element x, and by o(G) the quotient o(G)=\frac{\psi(G)}{|G|}. Confirming a conjecture posed by E.I. Khukhro, A. Moreto and M. Zarrin, we prove that if o(G)< o(A_5), then G is solvable.
Cite
@article{arxiv.2112.04220,
title = {Another criterion for solvability of finite groups},
author = {M. Herzog and P. Longobardi and M. Maj},
journal= {arXiv preprint arXiv:2112.04220},
year = {2021}
}