TY - JOUR
AU - M. R. Darafsheh
AU - P. Nosratpour
PY - 2012/02/25
Y2 - 2021/01/26
TI - Recognition of the groups $L_5(4)$ and $U_4(4)$ by the prime graph
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 64
IS - 2
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/2567
AB - Let $G$ be a finite group. The prime graph of $G$ is the graph $\Gamma(G)$ whose vertex set is the set $\Pi(G)$ of all prime divisors of the order $|G|$ and two distinct vertices $p$ and $q$ of which are adjacent by an edge if $G$ has an element of order $pq$. We prove that if $S$ denotes one of the simple groups $L_5(4)$ and $U_4(4)$ and if $G$ is a finite group with $\Gamma(G) = \Gamma(S)$, then $G$ has a$G$ normal subgroup $N$ such that $\Pi(N) \subseteq \{2, 3, 5\}$ and $\cfrac GN \cong S$.
ER -