A new characterization of PSL(2, 25)

Document Type : Research Paper


1 Babol Education, Mazandaran, Iran

2 Islamic Azad University Babol Branch


‎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) $‎.


Main Subjects

J. H. Conway, R. T. Curtis, S. P. Norton, et al (1985). Atlas of finite groups. Clarendon, Oxford. C. G. Shao, W. Shi, Q. Jiang (2008). Characterization of simple $% K_{4}- $groups. Front Math. China. 3, 355-370 R. Shen, C. G. Shao, Q. Jiang, W. Shi, V. Mazurov (2010). A New Characterization of $A_{5}$. Monatsh Math.. , 337-341 M. Khatami, B. Khosravi, Z. Akhlaghi (2009). A new characterization for some linear groups. Monatsh Math.. G. Frobenius (1895). Verallgemeinerung des sylowschen satze. Berliner sitz. , 981-993 M. Hall (1959). The Theory of Groups. Macmillan, New York. M. Herzog (1968). On finite simple groups of order divisible by three primes only. J. Algebra (10). 120, 383-388 W. Shi (1991). On simple $K_{4}$-groups. Chinese Science Bull. (17) (in Chinese).. 36, 1281-1283