Nonsolvable finite groups all of whose local subgroups are solvable
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- by John G. Thompson PDF
- Bull. Amer. Math. Soc. 74 (1968), 383-437
References
- J. L. Alperin, Centralizers of abelian normal subgroups of $p$-groups, J. Algebra 1 (1964), 110β113. MR 167528, DOI 10.1016/0021-8693(64)90027-4
- J. L. Alperin, Sylow intersections and fusion, J. Algebra 6 (1967), 222β241. MR 215913, DOI 10.1016/0021-8693(67)90005-1
- J. L. Alperin and Daniel Gorenstein, Transfer and fusion in finite groups, J. Algebra 6 (1967), 242β255. MR 215914, DOI 10.1016/0021-8693(67)90006-3
- Emil Artin, The orders of the classical simple groups, Comm. Pure Appl. Math. 8 (1955), 455β472. MR 73601, DOI 10.1002/cpa.3160080403
- Norman Blackburn, Generalizations of certain elementary theorems on $p$-groups, Proc. London Math. Soc. (3) 11 (1961), 1β22. MR 122876, DOI 10.1112/plms/s3-11.1.1
- N. Blackburn, On prime-power groups with two generators, Proc. Cambridge Philos. Soc. 54 (1958), 327β337. MR 102557, DOI 10.1017/s0305004100033521
- 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.Β 209β217. MR 0095203
- Richard Brauer, On finite Desarguesian planes. I, Math. Z. 90 (1965), 117β123. MR 193152, DOI 10.1007/BF01112235
- Richard Brauer, Some applications of the theory of blocks of characters of finite groups. II, J. Algebra 1 (1964), 307β334. MR 174636, DOI 10.1016/0021-8693(64)90011-0
- 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), 1757β1759. MR 109846, DOI 10.1073/pnas.45.12.1757
- Richard Brauer and Paul Fong, A characterization of the Mathieu group ${\mathfrak {M}}_{12}$, Trans. Amer. Math. Soc. 122 (1966), 18β47. MR 207817, DOI 10.1090/S0002-9947-1966-0207817-1
- Leonard Eugene Dickson, Linear groups: With an exposition of the Galois field theory, Dover Publications, Inc., New York, 1958. With an introduction by W. Magnus. MR 0104735
- Walter Feit, A characterization of the simple groups $\textrm {SL}(2,\,2^{a})$, Amer. J. Math. 82 (1960), 281β300. MR 113954, DOI 10.2307/2372736
- Paul Fong, Some Sylow subgroups of order $32$ and a characterization of $\textrm {U}(3,\,3)$, J. Algebra 6 (1967), 65β76. MR 206091, DOI 10.1016/0021-8693(67)90014-2 15. G. Frobenius and I. Schur, Ueber die reelen Darstellungen der endlichen Gruppen, Berliner Sitz. (1906), 186-208.
- George Glauberman, Central elements in core-free groups, J. Algebra 4 (1966), 403β420. MR 202822, DOI 10.1016/0021-8693(66)90030-5
- George Glauberman, A characteristic subgroup of a $p$-stable group, Canadian J. Math. 20 (1968), 1101β1135. MR 230807, DOI 10.4153/CJM-1968-107-2
- George Glauberman, On groups with a quaternion Sylow $2$-subgroup, Illinois J. Math. 18 (1974), 60β65. MR 332969 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.
- Daniel Gorenstein and John H. Walter, On the maximal subgroups of finite simple groups, J. Algebra 1 (1964), 168β213. MR 172917, DOI 10.1016/0021-8693(64)90032-8
- Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215 22. P. Hall, A characteristic property of soluble groups, J. London Math. Soc. 12(1937), 198-200.
- P. Hall, Theorems like Sylowβs, Proc. London Math. Soc. (3) 6 (1956), 286β304. MR 77533, DOI 10.1112/plms/s3-6.2.286 24. P. Hall, Lecture Notes (unpublished). 25. P. Hall, On a theorem of Frobenius, Proc. London Math. Soc. 40(1935), 468-501.
- P. Hall and Graham Higman, On the $p$-length of $p$-soluble groups and reduction theorems for Burnsideβs problem, Proc. London Math. Soc. (3) 6 (1956), 1β42. MR 72872, DOI 10.1112/plms/s3-6.1.1
- Graham Higman, Suzuki $2$-groups, Illinois J. Math. 7 (1963), 79β96. MR 143815
- Noboru ItΓ΄, On a theorem of H. F. Blichfeldt, Nagoya Math. J. 5 (1953), 75β77. MR 53934, DOI 10.1017/S0027763000015452
- B. H. Neumann, Groups with automorphisms that leave only the neutral element fixed, Arch. Math. (Basel) 7 (1956), 1β5. MR 74413, DOI 10.1007/BF01900516
- Rimhak Ree, A family of simple groups associated with the simple Lie algebra of type $(G_{2})$, Amer. J. Math. 83 (1961), 432β462. MR 138680, DOI 10.2307/2372888 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.
- Charles C. Sims, Graphs and finite permutation groups, Math. Z. 95 (1967), 76β86. MR 204509, DOI 10.1007/BF01117534
- Robert Steinberg, Generators for simple groups, Canadian J. Math. 14 (1962), 277β283. MR 143801, DOI 10.4153/CJM-1962-018-0
- Michio Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc. 99 (1961), 425β470. MR 131459, DOI 10.1090/S0002-9947-1961-0131459-5
- Michio Suzuki, Finite groups of even order in which Sylow 2-groups are independent, Ann. of Math. (2) 80 (1964), 58β77. MR 162841, DOI 10.2307/1970491
- Michio Suzuki, On a class of doubly transitive groups, Ann. of Math. (2) 75 (1962), 105β145. MR 136646, DOI 10.2307/1970423
- Michio Suzuki, On characterizations of linear groups. III, Nagoya Math. J. 21 (1962), 159β183. MR 142665, DOI 10.1017/S0027763000023813
- Michio Suzuki, Finite groups in which the centralizer of any element of order $2$ is $2$-closed, Ann. of Math. (2) 82 (1965), 191β212. MR 183773, DOI 10.2307/1970569
- Jacques Tits, ThΓ©orΓ¨me de Bruhat et sous-groupes paraboliques, C. R. Acad. Sci. Paris 254 (1962), 2910β2912 (French). MR 138706
- John G. Thompson, Fixed points of $p$-groups acting on $p$-groups, Math. Z. 86 (1964), 12β13. MR 168653, DOI 10.1007/BF01111272
- John G. Thompson, Normal $p$-complements for finite groups, J. Algebra 1 (1964), 43β46. MR 167521, DOI 10.1016/0021-8693(64)90006-7
- John G. Thompson, Factorizations of $p$-solvable groups, Pacific J. Math. 16 (1966), 371β372. MR 188296, DOI 10.2140/pjm.1966.16.371
- Helmut Wielandt, Beziehungen zwischen den Fixpunktzahlen von Automorphismengruppen einer eindlichen Gruppe, Math. Z 73 (1960), 146β158 (German). MR 0117286, DOI 10.1007/BF01162475
- W. J. Wong, On finite groups whose $2$-Sylow subgroups have cyclic subgroups of index $2$, J. Austral. Math. Soc. 4 (1964), 90β112. MR 0160816, DOI 10.1017/S1446788700022771 46. R. Zemlin, On a conjecture arising from a theorem of Frobenius, Ph.D. Thesis, Ohio State University, 1954 (unpublished).
Additional Information
- Journal: Bull. Amer. Math. Soc. 74 (1968), 383-437
- DOI: https://doi.org/10.1090/S0002-9904-1968-11953-6
- MathSciNet review: 0230809