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A new finite simple group with abelian Sylow 2-subgroups and its characterization. (English) Zbl 0214.28003


MSC:

20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure

Citations:

Zbl 0142.25903
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References:

[1] Brauer, K., Investigations on group characters, Ann. Math., 42, 936-958 (1941) · Zbl 0061.03702
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[4] Brauer, R.; Fowler, K. A., On groups of even order, Ann. Math., 62, 565-583 (1955) · Zbl 0067.01004
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[6] Coxeter, H. S.M, The abstract groups \(G^{m,n,p}\), Trans. Amer. Math. Soc., 45, 73-150 (1939) · Zbl 0020.20703
[7] Dickson, L. E., Linear Groups (1958), New York
[8] Gorenstein, D.; Walter, J. H., On finite groups with dihedral Sylow 2-Subgroups, Illinois J. Math., 6, 553-593 (1962) · Zbl 0126.05202
[9] Janko, Z., A new finite simple group with abelian 2-Sylow subgroups, (Proc. Nat. Acad. Sci. U.S.A., 53 (1965)), 657-658 · Zbl 0142.25903
[12] Schur, I., Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. für die reine Angew. Math., 132, 85-137 (1907) · JFM 38.0174.02
[13] Suzuki, M., On characterizations of linear groups. I, Trans. Amer. Math. Soc., 92, 191-204 (1959) · Zbl 0089.01605
[14] Suzuki, M., Applications of group characters, (Proc. Symp. Pure Math., 1 (1959)), 88-99
[15] Zassenhaus, H., (Lehrbuch der Gruppentheorie (1937), Teubner: Teubner Leipzig u. Berlin), 1956
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