TY - JOUR AU - M. R. Darafsheh AU - P. Nosratpour PY - 2016/08/25 Y2 - 2024/03/29 TI - Characterization of the group $G_2(5)$ by the prime graph JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 68 IS - 8 SE - Short communications DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1909 AB - Let $G$ be a finite group. The prime graph of $G$ is a graph $\Gamma (G)$ with vertex set $\pi (G)$ and the set of all prime divisorsof $|G|$, where two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. We prove that if$G\Gamma (G) = \Gamma (G_2(5))$, then $G$ has a normal subgroup $N$ such that $\pi (N) \subseteq \{ 2, 3, 5\}$ and $G/N \sim = G_2(5)$. ER -