Recognition by prime graph of the almost simple group PGL(2, 25)

Journal of Linear and Topological Algebra

مقاله 7، دوره 05، شماره 01، اردیبهشت 2016، صفحه 63-66   

نوع مقاله: Research Paper

نویسنده

A. Mahmoudifar^*

Department of Mathematics, Tehran-North Branch, Islamic Azad University, Tehran, Iran

چکیده

Throughout this paper, every groups are finite. The prime graph of a group $G$ is denoted by $\Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite 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.

کلیدواژه‌ها

linear group؛ Almost simple group؛ prime graph؛ element order؛ Frobenius group

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