| Abstract:
Let G be a nite group and let G(G) be the prime graph of G. Assume 2<q=pa< 100.
We determine finite groups G such that G (G) =G (U3 (q)) and prove that if q¹3; 5; 9; 17, then U3 (q) is quasirecognizable by prime graph, i.e. if G is a finite group with the same prime graph as the finite simple group U3 (q), then G has a unique non-Abelian composition factor isomorphic to U3 (q). As a consequence of our results, we prove that the simple groups U3 (8) and U3 (11) are 4-recognizable and 2-recognizable by prime graph, respectively. In fact, the group U3 (8) is the rst example which is a 4-recognizable by prime graph.
|