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Title

QUASIRECOGNITION BY PRIME GRAPH OF U3(Q) WHERE WHERE 2 < Q= Pα<100

Pages

 Start Page 51 | End Page 66

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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.

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