Authors
- P. Nosratpour ^{} ^{1}
- M. R. Darafsheh ^{2}
^{1} Department of mathematics, ILam Branch, Islamic Azad university, Ilam, Iran
^{2} School of Mathematics, statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
Abstract
Let $G$ be a finite group. The prime graph of $G$ is a graph $\Gamma(G)$ with vertex set $\pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. In this paper we prove that if $\Gamma(G)=\Gamma(G_2(5))$, then $G$ has a normal subgroup $N$ such that $\pi(N)\subseteq\{2,3,5\}$ and $G/N\equiv G_2(5)$.
Keywords
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