Mahmoudifar, A. (2016). Recognition by prime graph of the almost simple group PGL(2, 25). Journal of Linear and Topological Algebra (JLTA), 05(01), 63-66.
A. Mahmoudifar. "Recognition by prime graph of the almost simple group PGL(2, 25)". Journal of Linear and Topological Algebra (JLTA), 05, 01, 2016, 63-66.
Mahmoudifar, A. (2016). 'Recognition by prime graph of the almost simple group PGL(2, 25)', Journal of Linear and Topological Algebra (JLTA), 05(01), pp. 63-66.
Mahmoudifar, A. Recognition by prime graph of the almost simple group PGL(2, 25). Journal of Linear and Topological Algebra (JLTA), 2016; 05(01): 63-66.
Recognition by prime graph of the almost simple group PGL(2, 25)
Department of Mathematics, Tehran-North Branch, Islamic Azad University, Tehran, Iran
Abstract
Throughout this paper, every groups are fi nite. The prime graph of a group $G$ is denoted by $\Gamma(G)$. Also $G$ is called recognizable by prime graph if for every fi nite group $H$ with $\Gamma(H) = \Gamma(G)$, we conclude that $G\cong H$. Until now, it is proved that if $k$ is an odd number and $p$ is an odd prime number, then $PGL(2,p^k)$ is recognizable by prime graph. So if $k$ is even, the recognition by prime graph of $PGL(2,p^k)$, where $p$ is an odd prime number, is an open problem. In this paper, we generalize this result and we prove that the almost simple group $PGL(2,25)$ is recognizable by prime graph.
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