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

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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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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395–5746, Tehran, Iran

    Behrooz Khosravi

  2. Dept. of Pure Math., Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, 15914, Iran

    Hossein Moradi

Authors
  1. Behrooz Khosravi
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  2. Hossein Moradi
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Correspondence to Behrooz Khosravi.

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The first author was supported in part by a grant from IPM (89200113).

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Khosravi, B., Moradi, H. Quasirecognition by prime graph of finite simple groups L n (2) and U n (2). Acta Math Hung 132, 140–153 (2011). https://doi.org/10.1007/s10474-010-0053-3

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  • DOI: https://doi.org/10.1007/s10474-010-0053-3

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