QUASIRECOGNITION BY PRIME GRAPH OF U3(q) WHERE 2 < q = p < 100

Abstract. Let G be a finite group and let ??(G) be the prime graph of G. Assume 2 < q = p < 100. We determine finite groups G such that ??(G) = ??(U3(q)) and prove that if q?3,5,9,17 , then U_3(q) is quasirecognizable by prime graph, i.e. if G is a finite group with the same prime graph as the finite simple group U_3(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 U_3(8) and U_3(11) are 4-recognizable and 2-recognizable by prime graph, respectively. In fact, the group U_3(8) is the first example which is a 4-recognizable by prime graph.