A new characterization of $PSL(2, 25)$

Document Type: Research Paper

Authors

1 Babol Education, Mazandaran, Iran

2 Islamic Azad University Babol Branch

Abstract

‎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) $‎.

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