TY - JOUR
AU - M. R. Darafsheh
AU - P. Nosratpour
PY - 2016/08/25
Y2 - 2022/10/06
TI - Characterization of the group $G_2(5)$ by the prime graph
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 68
IS - 8
SE - Short communications
DO -
UR - http://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 -