Characterizations of some groups by their sizes of the subset of pairwise non-commuting elements. (Q2883280)

Let \(G\) be a finite non-Abelian group. The maximum size of a set of elements of the group \(G\) whose elements are pairwise non-commuting will be denoted by \(\omega(G)\). It is proved by \textit{A. Abdollahi} and \textit{A. Mohammadi Hassanabadi} [Bull. Iran. Math. Soc. 30, No. 2, 1-20 (2004; Zbl 1091.20026)] that for a non-solvable group \(G\), \(\omega(G)\leq 21\) if and only if \(G\cong Z(G)\times A_5\). The structure of non-solvable groups \(G\) with \(\omega(G)\leq 57\) is determined by \textit{A. Abdollahi, A. Azad, A. Mohammadi Hassanabadi} and \textit{M. Zarrin} [Algebra Colloq. 17, No. 4, 611-620 (2010; Zbl 1227.20021)].NEWLINENEWLINE The main result of the paper under review is the following. Theorem 1.1. Let \(G\) be a finite non-Abelian simple group such that \(\omega(G)\leq 91\). Then \(G\) is isomorphic to \(A_5\), \(A_6\) or \(\text{PSL}(2,7)\).