×

zbMATH — the first resource for mathematics

Finite groups with a split BN-pair of rank 1. I. (English) Zbl 0244.20003

MSC:
20B20 Multiply transitive finite groups
20D05 Finite simple groups and their classification
20G40 Linear algebraic groups over finite fields
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alperin, J.L.; Brauer, R.; Gorenstein, D., Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups, Trans. amer. math. soc., 151, 1-261, (1970) · Zbl 0222.20002
[2] \scJ. L. Alperin, R. Brauer, and D. Gorenstein, Finite simple groups of 2-rank two, to appear. · Zbl 0274.20021
[3] Alperin, J.L.; Gorenstein, D., The multiplicators of certain simple groups, (), 515-519 · Zbl 0151.02002
[4] Bender, H., Endliche Zweifach transitive permutationsgruppen, deren involutionen keine fixpunkte haben, Math. Z., 104, 175-204, (1968) · Zbl 0172.02803
[5] Birkhoff, G.D.; Vandiver, H.S., On the integral divisors of an −bn, Ann. of math., 5, 173-180, (1904)
[6] Brauer, R.; Fong, P., A characterization of the Mathieu group M12, Trans. amer. math. soc., 122, 18-47, (1966) · Zbl 0138.02503
[7] Burgoyne, N.; Fong, P., The Schur multipliers of the Mathieu groups, Nagoya math. J., 27, 733-745, (1966) · Zbl 0171.28801
[8] Burnside, W., Theory of groups of finite order, (1955), Dover New York · Zbl 0064.25105
[9] Dickson, L.E., Linear groups, (1958), Dover New York
[10] Feit, W., On a class of doubly transitive permutation groups, Illinois J. math., 4, 170-186, (1960) · Zbl 0098.25202
[11] Feit, W.; Thompson, J.G., Solvability of groups of odd order, Pacific J. math., 13, 771-1029, (1963) · Zbl 0124.26402
[12] Fong, P.; Wong, W., A characterization of the finite simple groupspsp(4, q), G2(q), D42(q), I, Nagoya math. J., 36, 143-184, (1969) · Zbl 0188.06402
[13] Glauberman, G., Central elements in core-free groups, J. algebra, 4, 403-420, (1966) · Zbl 0145.02802
[14] Hall, M., The theory of groups, (1959), MacMillan New York
[15] Harada, K., A characterization of the simple group U3(5), Nagoya math. J., 38, 27-40, (1970) · Zbl 0214.28002
[16] Harada, K., On some doubly transitive groups, J. algebra, 17, 437-450, (1971) · Zbl 0238.20010
[17] Hering, C., Zweifach transitive permutationsgruppen, in denen zwei die maximale anzahl von fixpunkten von involutionen ist, Math. Z., 104, 150-174, (1968) · Zbl 0172.02804
[18] Hering, C., Über projektive ebenen vom Lenz-typ III, Math. Z., 105, 219-225, (1968) · Zbl 0167.18801
[19] Huppert, B., Zweifach transitive auflösbare permutationsgruppen, Math. Z., 68, 126-150, (1957) · Zbl 0079.25502
[20] Ito, N., On a class of doubly transitive permutation groups, Illinois J. math., 6, 341-352, (1962) · Zbl 0105.25501
[21] Ito, N., On doubly transitive groups of degree n and order 2(n − 1)n, Nagoya math. J., 27, 409-417, (1966) · Zbl 0139.25102
[22] \scW. M. Kantor, M. E. O’Nan, and G. M. Seitz, 2-Transitive groups in which the stabilizer of two points is cyclic, J. Algebra, to appear.
[23] Nagao, H., On multiply transitive groups I, Nagoya math. J., 27, 15-19, (1966) · Zbl 0143.04302
[24] O’Nan, M.E., A characterization of the three-dimensional protective unitary group over a finite field, () · Zbl 0639.20002
[25] Passman, D.S., Permutation groups, (1968), Benjamin New York · Zbl 0164.33805
[26] Passman, D.S., Some 5/2 transitive permutation groups, Pacific J. math., 28, 157-171, (1969) · Zbl 0172.02802
[27] Ree, R., A family of simple groups associated with the simple Lie algebra of type (G2), Amer. J. math., 83, 432-462, (1961) · Zbl 0104.24705
[28] Ree, R., Sur une famille de groupes de permutations doublement transitifs, Canad. J. math., 16, 797-820, (1964) · Zbl 0126.05301
[29] Schur, I., Untersuchungenüber die darstellungen der endlichen gruppen durch gebrochene lineare substitutionen, J. reine angew. math., 132, 85-137, (1907) · JFM 38.0174.02
[30] \scE. Shult, On the fusion of an involution in its centralizer, to appear.
[31] \scE. Shult, On a class of doubly transitive groups, to appear. · Zbl 0241.20004
[32] Steinberg, R., Automorphisms of finite linear groups, Canad. J. math., 12, 606-615, (1960) · Zbl 0097.01703
[33] Suzuki, M., On a class of doubly transitive groups, Ann. of math., 75, 105-145, (1962) · Zbl 0106.24702
[34] Suzuki, M., On a class of doubly transitive groups: II, Ann. of math., 79, 514-589, (1964) · Zbl 0123.25101
[35] Suzuki, M., A characterization of the 3-dimensional projective unitary group over a field of odd characteristic, J. algebra, 2, 1-14, (1965) · Zbl 0134.03102
[36] Suzuki, M., Transitive extensions of a class of doubly transitive groups, Nagoya math. J., 27, 159-169, (1966) · Zbl 0146.03803
[37] Thompson, J.G., Finite groups with fixed-point-free automorphisms of prime order, (), 578-581 · Zbl 0086.25101
[38] \scJ. Tits, Buildings and BN-pairs of spherical type. Lecture notes. Berlin-Heidelberg-New York: Springer, to appear. · Zbl 0295.20047
[39] Walter, J., The characterization of finite groups with abelian Sylow 2-subgroups, Ann. of math., 89, 405-514, (1969) · Zbl 0184.04605
[40] Ward, H.N., On Ree’s series of simple groups, Trans. amer. math. soc., 121, 62-89, (1966) · Zbl 0139.24902
[41] Wielandt, H., Beziehungen zwischen den fixpunktanzahlen von automorphismengruppen einer endlichen gruppe, Math. Z., 73, 146-158, (1960) · Zbl 0093.02302
[42] Wielandt, H., Finite permutation groups, (1964), Academic Press New York · Zbl 0138.02501
[43] Zassenhaus, H., Kennzeichnung endlicher linearer gruppen als permutationsgruppen, (), 17-40 · Zbl 0011.24904
[44] Zassenhaus, H., Über endliche fastkörper, (), 187-220 · JFM 61.0126.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.