Recognition of the groups L₅(4) and U₄(4) by the prime graph - Nosratpour, P.; Darafsheh, M.R. (Український математичний журнал, 2012)
Let G be a finite group. The prime graph of G is the graph Γ(G) whose set of vertices is the set Π(G) of all prime divisors of the order |G| and two different vertices p and q of which are connected by an edge if G has an element of order pq. We prove that if S is one of the simple groups L₅(4) and U₄(4) and G is a finite group with Γ(G) = Γ(S), then G has a normal subgroup N such that Π(N) ⊆ {2, 3, 5} and G/N≅S.