Let G be a finite group. Denote by psi (G) the sum psi(G) =Sigma (x is an element of G) |x|, where |x| denotes the order of the element x, and by o(G) the quotient o(G) =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. (c) 2022 Elsevier Inc. All rights reserved.
Another criterion for solvability of finite groups
Marcel Herzog;Patrizia Longobardi;Mercede Maj
2022-01-01
Abstract
Let G be a finite group. Denote by psi (G) the sum psi(G) =Sigma (x is an element of G) |x|, where |x| denotes the order of the element x, and by o(G) the quotient o(G) =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. (c) 2022 Elsevier Inc. All rights reserved.File in questo prodotto:
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