Recognition of the groups $L_5(4)$ and $U_4(4)$ by the prime graph - Darafsheh, M. R.; Nosratpour, P. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
Let $G$ be a finite group. The prime graph of $G$ is the graph $Γ(G)$ whose vertex set is the set $Π(G)$ 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 $Γ(G) = Γ(S)$, then $G$ has a$G$ normal subgroup $N$ such that $Π(N) \subseteq \{2, 3, 5\}$ and $\cfrac GN \cong S$.