On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$

Journal of Linear and Topological Algebra

مقاله 4، دوره 06، شماره 03، آذر 2017، صفحه 217-221   

نوع مقاله: Research Paper

نویسنده

A. Mahmoudifar^*

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

چکیده

The prime graph of a finite group $G$ is denoted by $\Gamma(G)$ whose vertex set is $\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $\Gamma(H)=\Gamma(G)$, in while $H\not\cong G$. In this paper, we consider finite groups with the same prime graph as the almost simple group $\textrm{PGL}(2,49)$. Moreover, we construct some Frobenius groups whose prime graphs coincide with $\Gamma(\textrm{PGL}(2,49))$, in particular, we get that $\textrm{PGL}(2,49)$ is unrecognizable by its prime graph.

کلیدواژه‌ها

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

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