University of Isfahan International Journal of Group Theory 2251-7650 5 1 2016 03 01 A characterization of L2(81) by nse 29 35 5843 10.22108/ijgt.2016.5843 EN Leila Mousavi Department of Mathematical Sciences; Isfahan University of Technology; Isfahan 84156-83111; Iran. Bijan Taeri Department of Mathematical Sciences;, Isfahan University of Technology Journal Article 2014 03 07 Let $\pi_e(G)$ be the set of element orders of a finite group $G$‎. ‎Let $nse(G)=\{m_n\mid n\in\pi_e(G)\}$‎, ‎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 $G\cong L_2(81)$‎. ‎set of the numbers of elements of the same order‎ ‎order of an element‎ ‎Thompson's problem https://ijgt.ui.ac.ir/article_5843_2a42ff7ced0280cc4820db4840f4709b.pdf