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A Characterization of the Finite Simple Groups PSp(4,q), G2(q), D42(q), II

Published online by Cambridge University Press:  22 January 2016

Paul Fong
Paul Fong*
Affiliation:
University of Illinois, Chicago, Illinois
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Our object in this paper is to prove the following result.

THEOREM. Let G be a finite group satisfying the following conditions:

  • (*) G has subgroups L1, L2 such that L1 ≃ SL(2, q1), L2 ≃ SL(2, q2), [L1 L2] = 1, , where j is an involution, and |C(j): L1L2| = 2.

  • (**) where n2 = 1,

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 39 , August 1970 , pp. 39 - 79
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Brauer, R. and Fong, P., A characterization of the Mathieu group M12 , Transactions of the Amer. Math. Soc. 122 (1966), 18–47.Google Scholar
[2] Chevalley, C., Sur certains groupes simples, Tohoku Math. Journal (2), 7 (1955), 14–66.Google Scholar
[3] Dickson, L.E., Linear groups in an arbitrary field, Transactions of the Amer. Math. Soc. 2 (1901), 363–394.Google Scholar
[4] Dickson, L.E., A new system of simple groups, Math. Annalen, 60 (1905), 137–150.Google Scholar
[5] Fong, P. and Wong, W.J., A characterization of the finite simple groups PSp(4, q), G2(q) , , I, Nagoya Math. Journal 36 (1969), 143–184.Google Scholar
[6] Gorenstein, D., Finite groups. Harper and Row, New York, 1968.Google Scholar
[7] Janko, Z., A characterization of the simple group G2(3), Journal of Algebra 12 (1969), 360–371.Google Scholar
[8] Steinberg, R., Variations on a theme of Chevalley, Pac. Jour. Math. 9 (1959), 875–891.Google Scholar
[9] Suzuki, M., Applications of group characters, Proc. Symposium Pure Math., Amer. Math. Soc. 1 (1959) 88–99.Google Scholar
[10] Thomas, G., A characterization of the groups G2(2n) , Journal of Algebra 13 (1969), 87–118.Google Scholar
[11] Thompson, J.G., Non-solvable finite groups all of whose local subgroups are solvable, to appear.Google Scholar
[12] Tits, J., Théorème de Bruhat et sous-groupes paraboliques, C.R. Acad. Sci. Paris, 254 (1962), 2910–2912.Google Scholar
[13] Tits, J., Sur la trialité et certains groupes qui s’en déduisent, Institut des Hautes Études Scientifiques, 2 (1959).Google Scholar
[14] Wielandt, H., Zum Satz von Sylow, Math. Zeitschrift, 60 (1954), 407–409.Google Scholar
[15] Wong, W.J., A characterization of the finite projective symplectic groups PSp4(q) , Transactions of the Amer. Math. Soc. 139 (1969), 1–135.Google Scholar