Research Article

Geometric mean Sylow numbers of nonsolvable groups

Published in: Quaestiones Mathematicae
Volume 48 , issue 6 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 903–908
DOI: 10.2989/16073606.2025.2459360
Author(s): Chimere Stanley Anabanti University of Pretoria, South Africa, Alireza Khalili Asboei Farhangian University, Iran,
Keywords: 05E16, 20D10, 20D20, 20D60, Finite groups, nonsolvable groups, Sylow number,
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Abstract

Let G be a finite group. We write gsn(G) for the geometric mean Sylow number of G. The Fitting subgroup of G is denoted by F(G). It was recently proved that if gsn(G) < , then G is solvable. In this paper, we extend the study to nonsolvable groups. We prove that if G is a finite nonsolvable group, then the following holds:
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