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A Characterization of the finite simple group L4(3)

Published online by Cambridge University Press:  09 April 2009

Kok-Wee Phan
Affiliation:
Monash UniversityClayton, Australia
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In this paper we aim to give a characterization of the finite simple group L4(3) (i.e. PSL(4, 3)) by the structure of the centralizer of an involution contained in the centre of its Sylow 2-subgroup. More precisely, we shall prove the following result.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Artin, E., Geometric Algebra, Wiley-Interscience (1957).Google Scholar
[2]Brauer, R. and Suzuki, M., ‘On finite groups of even order whose 2-Sylow group is a quaternion group’, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 17571759.CrossRefGoogle Scholar
[3]Gorenstein, D. and Walter, J. H., ‘On finite groups with dihedral Sylow 2-subgroups’, Illionis J. Math. 6 (1962), 553593.Google Scholar
[4]Hall, M. Jr, The Theory of Groups, MacMillan (1959).Google Scholar
[5]Higman, D. G., ‘Focal series in finite groups’, Cand. J. Math. 5 (1953), 477497.CrossRefGoogle Scholar
[6]Janko, Z., ‘A characterization of the finite simple groups PSρ 4(3)’, (to appear).Google Scholar
[7]Thompson, J. G., ‘Non-solvable finite groups whose non-identity solvable subgroups have solvable normalizers’, (to appear).Google Scholar
[8]Tits, M. Jacques, ‘Théorème de Bruhat et sous-groupes paraboliques’, C. R. Acad. Sci. Paris, 254 (1962), 29102912.Google Scholar
[9]Suzuki, M., ‘On characterization of linear groups’, I. Trans. Amer. Math. Soc. 92 (1959).Google Scholar
[10]Wielandt, H., ‘Beziehungen zwischen der Fixpunktzahlen von Automorphismengruppen einer endlichen Gruppe’, Math. Zeit. 73 (1960), 146158.CrossRefGoogle Scholar