Quasirecognition by prime graph of finite simple groups L n (2) and U n (2)

Author： Khosravi Behrooz   Moradi Hossein  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.132, Iss.1-2, 2011-07, pp. : 140-153

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Abstract

Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, p′ are joined by an edge if G has an element of order pp′. Let L=L n (2) or U n (2), where n≧17. We prove that L is quasirecognizable by prime graph, i.e. if G is a finite group such that Γ(G)=Γ(L), then G has a unique nonabelian composition factor isomorphic to L. As a consequence of our result we give a new proof for the recognition by element orders of L n (2). Also we conclude that the simple group U n (2) is quasirecognizable by element orders.

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