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) {2, 3, 5} and GN S.