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Quasirecognition by prime graph of the simple group 2 F 4(q)

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Abstract

As the main result, we show that if G is a finite group such that Γ(G) = Γ(2 F 4(q)), where q = 22m+1 for some m ≧ 1, then G has a unique nonabelian composition factor isomorphic to 2 F 4(q). We also show that if G is a finite group satisfying |G| =|2 F 4(q)| and Γ(G) = Γ(2 F 4(q)), then G ≅ 2 F 4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2 F 4(q).

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Authors and Affiliations

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

    Z. Akhlaghi, M. Khatami & B. Khosravi

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

    B. Khosravi

Authors
  1. Z. Akhlaghi
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  2. M. Khatami
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  3. B. Khosravi
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Correspondence to B. Khosravi.

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The third author was supported in part by a grant from IPM (No. 87200022).

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Akhlaghi, Z., Khatami, M. & Khosravi, B. Quasirecognition by prime graph of the simple group 2 F 4(q). Acta Math Hung 122, 387–397 (2009). https://doi.org/10.1007/s10474-009-8048-7

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  • DOI: https://doi.org/10.1007/s10474-009-8048-7

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