×

zbMATH — the first resource for mathematics

Nonsolvable finite groups all of whose local subgroups are solvable. (English) Zbl 0159.30804

MSC:
20D05 Finite simple groups and their classification
Keywords:
group theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. L. Alperin, Centralizers of abelian normal subgroups of \?-groups, J. Algebra 1 (1964), 110 – 113. · Zbl 0119.02901 · doi:10.1016/0021-8693(64)90027-4 · doi.org
[2] J. L. Alperin, Sylow intersections and fusion, J. Algebra 6 (1967), 222 – 241. · Zbl 0168.27202 · doi:10.1016/0021-8693(67)90005-1 · doi.org
[3] J. L. Alperin and Daniel Gorenstein, Transfer and fusion in finite groups, J. Algebra 6 (1967), 242 – 255. · Zbl 0168.27203 · doi:10.1016/0021-8693(67)90006-3 · doi.org
[4] Emil Artin, The orders of the classical simple groups, Comm. Pure Appl. Math. 8 (1955), 455 – 472. · Zbl 0065.25703 · doi:10.1002/cpa.3160080403 · doi.org
[5] Norman Blackburn, Generalizations of certain elementary theorems on \?-groups, Proc. London Math. Soc. (3) 11 (1961), 1 – 22. · Zbl 0102.01903 · doi:10.1112/plms/s3-11.1.1 · doi.org
[6] N. Blackburn, On prime-power groups with two generators, Proc. Cambridge Philos. Soc. 54 (1958), 327 – 337. · Zbl 0083.01902
[7] Richard Brauer, On the structure of groups of finite order, Proceedings of the International Congress of Mathematicians, Amsterdam, 1954, Vol. 1, Erven P. Noordhoff N.V., Groningen; North-Holland Publishing Co., Amsterdam, 1957, pp. 209 – 217.
[8] Richard Brauer, On finite Desarguesian planes. I, Math. Z. 90 (1965), 117 – 123. · Zbl 0132.40703 · doi:10.1007/BF01112235 · doi.org
[9] Richard Brauer, Some applications of the theory of blocks of characters of finite groups. II, J. Algebra 1 (1964), 307 – 334. · Zbl 0214.28102 · doi:10.1016/0021-8693(64)90011-0 · doi.org
[10] Richard Brauer and Michio Suzuki, On finite groups of even order whose 2-Sylow group is a quaternion group, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 1757 – 1759. · Zbl 0090.01901
[11] Richard Brauer and Paul Fong, A characterization of the Mathieu group \?\(_{1}\)\(_{2}\), Trans. Amer. Math. Soc. 122 (1966), 18 – 47. · Zbl 0138.02503
[12] Leonard Eugene Dickson, Linear groups: With an exposition of the Galois field theory, with an introduction by W. Magnus, Dover Publications, Inc., New York, 1958. · Zbl 0082.24901
[13] Walter Feit, A characterization of the simple groups \?\?(2,2^\?), Amer. J. Math. 82 (1960), 281 – 300. · Zbl 0103.01401 · doi:10.2307/2372736 · doi.org
[14] Paul Fong, Some Sylow subgroups of order 32 and a characterization of \?(3,3), J. Algebra 6 (1967), 65 – 76. · Zbl 0183.03103 · doi:10.1016/0021-8693(67)90014-2 · doi.org
[15] G. Frobenius and I. Schur, Ueber die reelen Darstellungen der endlichen Gruppen, Berliner Sitz. (1906), 186-208. · JFM 37.0161.01
[16] George Glauberman, Central elements in core-free groups, J. Algebra 4 (1966), 403 – 420. · Zbl 0145.02802 · doi:10.1016/0021-8693(66)90030-5 · doi.org
[17] George Glauberman, A characteristic subgroup of a \?-stable group, Canad. J. Math. 20 (1968), 1101 – 1135. · Zbl 0164.02202 · doi:10.4153/CJM-1968-107-2 · doi.org
[18] George Glauberman, On groups with a quaternion Sylow 2-subgroup, Illinois J. Math. 18 (1974), 60 – 65. · Zbl 0273.20006
[19] D. Gorenstein and J. Walter, The characterization of finite groups with dihedral Sylow 2-groups, J. Algebra (2) (1965), 85-151, 218-270, 354-393. · Zbl 0192.11902
[20] Daniel Gorenstein and John H. Walter, On the maximal subgroups of finite simple groups, J. Algebra 1 (1964), 168 – 213. · Zbl 0119.26803 · doi:10.1016/0021-8693(64)90032-8 · doi.org
[21] Marshall Hall Jr., The theory of groups, The Macmillan Co., New York, N.Y., 1959.
[22] P. Hall, A characteristic property of soluble groups, J. London Math. Soc. 12(1937), 198-200. · JFM 63.0069.02
[23] P. Hall, Theorems like Sylow’s, Proc. London Math. Soc. (3) 6 (1956), 286 – 304. · Zbl 0075.23907 · doi:10.1112/plms/s3-6.2.286 · doi.org
[24] P. Hall, Lecture Notes (unpublished).
[25] P. Hall, On a theorem of Frobenius, Proc. London Math. Soc. 40(1935), 468-501. · JFM 61.1017.02
[26] P. Hall and Graham Higman, On the \?-length of \?-soluble groups and reduction theorems for Burnside’s problem, Proc. London Math. Soc. (3) 6 (1956), 1 – 42. · Zbl 0073.25503 · doi:10.1112/plms/s3-6.1.1 · doi.org
[27] Graham Higman, Suzuki 2-groups, Illinois J. Math. 7 (1963), 79 – 96. · Zbl 0112.02107
[28] Noboru Itô, On a theorem of H. F. Blichfeldt, Nagoya Math. J. 5 (1953), 75 – 77. · Zbl 0052.26002
[29] B. H. Neumann, Groups with automorphisms that leave only the neutral element fixed, Arch. Math. (Basel) 7 (1956), 1 – 5. · Zbl 0070.02203 · doi:10.1007/BF01900516 · doi.org
[30] Rimhak Ree, A family of simple groups associated with the simple Lie algebra of type (\?\(_{2}\)), Amer. J. Math. 83 (1961), 432 – 462. · Zbl 0104.24705 · doi:10.2307/2372888 · doi.org
[31] J. Rust, On a conjecture of Frobenius, Ph.D. Thesis, University of Chicago, 1966.
[32] I. Schur, Zur Theorie der vertauschbaren Matrizen, J. Reine Angew. Math. 130 (1905), 66-76. · JFM 36.0140.01
[33] Charles C. Sims, Graphs and finite permutation groups, Math. Z. 95 (1967), 76 – 86. · Zbl 0244.20001 · doi:10.1007/BF01117534 · doi.org
[34] Robert Steinberg, Generators for simple groups, Canad. J. Math. 14 (1962), 277 – 283. · Zbl 0103.26204 · doi:10.4153/CJM-1962-018-0 · doi.org
[35] Michio Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc. 99 (1961), 425 – 470. · Zbl 0101.01604
[36] Michio Suzuki, Finite groups of even order in which Sylow 2-groups are independent, Ann. of Math. (2) 80 (1964), 58 – 77. · Zbl 0122.03202 · doi:10.2307/1970491 · doi.org
[37] Michio Suzuki, On a class of doubly transitive groups, Ann. of Math. (2) 75 (1962), 105 – 145. · Zbl 0106.24702 · doi:10.2307/1970423 · doi.org
[38] Michio Suzuki, On characterizations of linear groups. III, Nagoya Math. J. 21 (1962), 159 – 183. · Zbl 0106.25102
[39] Michio Suzuki, Finite groups in which the centralizer of any element of order 2 is 2-closed, Ann. of Math. (2) 82 (1965), 191 – 212. · Zbl 0132.01704 · doi:10.2307/1970569 · doi.org
[40] Jacques Tits, Théorème de Bruhat et sous-groupes paraboliques, C. R. Acad. Sci. Paris 254 (1962), 2910 – 2912 (French). · Zbl 0105.02201
[41] John G. Thompson, Fixed points of \?-groups acting on \?-groups, Math. Z. 86 (1964), 12 – 13. · Zbl 0132.01601 · doi:10.1007/BF01111272 · doi.org
[42] John G. Thompson, Normal \?-complements for finite groups, J. Algebra 1 (1964), 43 – 46. · Zbl 0119.26802 · doi:10.1016/0021-8693(64)90006-7 · doi.org
[43] John G. Thompson, Factorizations of \?-solvable groups, Pacific J. Math. 16 (1966), 371 – 372. · Zbl 0136.28502
[44] Helmut Wielandt, Beziehungen zwischen den Fixpunktzahlen von Automorphismengruppen einer eindlichen Gruppe, Math. Z 73 (1960), 146 – 158 (German). · Zbl 0093.02302 · doi:10.1007/BF01162475 · doi.org
[45] W. J. Wong, On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2, J. Austral. Math. Soc. 4 (1964), 90 – 112. · Zbl 0203.02901
[46] R. Zemlin, On a conjecture arising from a theorem of Frobenius, Ph.D. Thesis, Ohio State University, 1954 (unpublished).
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.