Recognition of the groups [L.sub.5] by the prime graph

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 [absolute value of 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 [L.sub.5](4) and [U.sub.4](4) and G is a finite group with Γ(G) = Γ(S), then G has a normal subgroup N such that Π(N) [subset or equal to] {2, 3, 5} and G/N ≡ S.