Characterization of the group $G_2(5)$ by the prime graph

• Date: 2016
• Main Authors: Darafsheh, M. R., Nosratpour, P., Дарафшех, М. Р., Носратпур, П.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1909
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 divisors of $|G|$, 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...