Another criterion for solvability of finite groups

2021/12/08 by M. Herzog, Herzog, M., P. Longobardi +3
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2112.04220

Abstract

Let G be a finite group. Denote by ψ(G) the sum ψ(G)=∑_{x∈ G}|x| where |x| denotes the order of the element x, and by o(G) the quotient o(G)=(ψ(G))/(|G|). Confirming a conjecture posed by E.I. Khukhro, A. Moreto and M. Zarrin, we prove that if o(G)< o(A₅), then G is solvable.

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