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

Mahmoudifar, A.

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	Recognition by prime graph of the almost simple group PGL(2, 25)
Article 7, Volume 05, Issue 01, Winter 2016, Page 63-66 PDF (107.36 K)
Document Type: Research Paper
Author
A. Mahmoudifar
Department of Mathematics, Tehran-North Branch, Islamic Azad University, Tehran, Iran
Abstract
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.
Keywords
linear group; Almost simple group; prime graph; element order; Frobenius group
Main Subjects
Group theory and generalizations


References
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