University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 A new characterization of PSL(2, 25) 15 19 765 10.22108/ijgt.2012.765 EN Alireza Khalili Asboei Babol Education, Mazandaran, Iran Syyed Sadegh Salehi Amiri Islamic Azad University Babol Branch Journal Article 2012 01 15 ‎Let $G$ be a finite group and $\pi_{e}(G)$ be the set of element‎ ‎orders of $G$‎. ‎Let $k \in \pi_{e}(G)$ and $m_{k}$ be the number of‎ ‎elements of order $k$ in $G$‎. ‎Set nse($G$):=$\{ m_{k} | k \in‎ ‎\pi_{e}(G)\}$‎. ‎In this paper‎, ‎we prove that if $G$ is a group such‎ ‎that nse($G$)=nse($PSL(2‎, ‎25)$)‎, ‎then $G \cong PSL(2‎, ‎25) $‎. Element order set of the numbers of elements of the same order Sylow subgroup https://ijgt.ui.ac.ir/article_765_3cb589fd74c1a6fe0587c1d1dc0a64f1.pdf