A characterization of $L_2(81)$ by nse

Abstract

Let $pi_e(G)$ be the set of element orders of a finite group $G$‎. ‎Let $nse(G)={m_nmid ninpi_e(G)}$‎, ‎where $m_n$ be the number of elements of order $n$ in $G$‎. ‎In this paper‎, ‎we prove that if $nse(G)=nse(L_2(81))$‎, ‎then $Gcong L_2(81)$‎.

Keywords

• ‎Set of the numbers of elements of the same order‎
• ‎order of an element‎
• ‎Thompson's problem