Mahmoudifar, A. (2017). On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$. Journal of Linear and Topological Algebra (JLTA), 06(03), 217-221.

A. Mahmoudifar. "On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$". Journal of Linear and Topological Algebra (JLTA), 06, 03, 2017, 217-221.

Mahmoudifar, A. (2017). 'On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$', Journal of Linear and Topological Algebra (JLTA), 06(03), pp. 217-221.

Mahmoudifar, A. On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$. Journal of Linear and Topological Algebra (JLTA), 2017; 06(03): 217-221.

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

^{}Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran, Iran

Abstract

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.

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