Another criterion for solvability of finite groups

Marcel Herzog, Patrizia Longobardi, Mercede Maj*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 [Formula presented] 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.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Algebra
StatePublished - 1 May 2022


  • Average order
  • Element orders
  • Simple groups
  • Soluble groups


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