Classifying the finite simple groups
HTML articles powered by AMS MathViewer
- by Daniel Gorenstein PDF
- Bull. Amer. Math. Soc. 14 (1986), 1-98
References
- J. L. Alperin, Sylow intersections and fusion, J. Algebra 6 (1967), 222–241. MR 215913, DOI 10.1016/0021-8693(67)90005-1
- J. L. Alperin, Richard Brauer, and Daniel Gorenstein, Finite groups with quasi-dihedral and wreathed Sylow $2$-subgroups, Trans. Amer. Math. Soc. 151 (1970), 1–261. MR 284499, DOI 10.1090/S0002-9947-1970-0284499-5
- J. L. Alperin, Richard Brauer, and Daniel Gorenstein, Finite simple groups of $2$-rank two, Scripta Math. 29 (1973), no. 3-4, 191–214. MR 401902
- Michael Aschbacher, Finite groups with a proper $2$-generated core, Trans. Amer. Math. Soc. 197 (1974), 87–112. MR 364427, DOI 10.1090/S0002-9947-1974-0364427-8
- Michael Aschbacher, On finite groups generated by odd transpositions. I, Math. Z. 127 (1972), 45–56. MR 310058, DOI 10.1007/BF01110103
- Michael Aschbacher, On finite groups of component type, Illinois J. Math. 19 (1975), 87–115. MR 376843
- Michael Aschbacher, A characterization of Chevalley groups over fields of odd order, Ann. of Math. (2) 106 (1977), no. 2, 353–398. MR 498828, DOI 10.2307/1971100
- Michael Aschbacher, Finite groups in which the generalized Fitting group of the centralizer of some involution is symplectic but not extraspecial, Comm. Algebra 4 (1976), no. 7, 595–616. MR 407144, DOI 10.1080/00927877608822122
- Michael Aschbacher, On finite groups in which the generalized Fitting group of the centralizer of some involution is extraspecial, Illinois J. Math. 21 (1977), no. 2, 347–364. MR 442089
- Michael Aschbacher, On the failure of the Thompson factorization in $2$-constrained groups, Proc. London Math. Soc. (3) 43 (1981), no. 3, 425–449. MR 635564, DOI 10.1112/plms/s3-43.3.425
- Michael Aschbacher, A characterization of certain Chevalley groups and its application to component type groups, Proceedings of the Conference on Finite Groups (Univ. Utah, Park City, Utah, 1975) Academic Press, New York, 1976, pp. 3–11. MR 0401903
- M. Aschbacher, On the maximal subgroups of the finite classical groups, Invent. Math. 76 (1984), no. 3, 469–514. MR 746539, DOI 10.1007/BF01388470
- Michael Aschbacher, Thin finite simple groups, J. Algebra 54 (1978), no. 1, 50–152. MR 511458, DOI 10.1016/0021-8693(78)90022-4
- Michael Aschbacher, Finite groups of rank $3$. I, Invent. Math. 63 (1981), no. 3, 357–402. MR 620676, DOI 10.1007/BF01389061
- Michael Aschbacher, Weak closure in finite groups of even characteristic, J. Algebra 70 (1981), no. 2, 561–627. MR 623826, DOI 10.1016/0021-8693(81)90236-2
- Michael Aschbacher, The uniqueness case for finite groups. I, Ann. of Math. (2) 117 (1983), no. 2, 383–454. MR 690850, DOI 10.2307/2007081
- M. Aschbacher, Subgroup structure of finite groups, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 35–44. MR 817233
- M. Aschbacher, Subgroup structure of finite groups, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 35–44. MR 817233
- Michael Aschbacher, Overgroups of Sylow subgroups in sporadic groups, Mem. Amer. Math. Soc. 60 (1986), no. 343, iv+235. MR 831891, DOI 10.1090/memo/0343
- Michael Aschbacher, Daniel Gorenstein, and Richard Lyons, The embedding of $2$-locals in finite groups of characteristic $2$-type. I, Ann. of Math. (2) 114 (1981), no. 2, 335–404. MR 632843, DOI 10.2307/1971297
- M. Aschbacher and L. Scott, Maximal subgroups of finite groups, J. Algebra 92 (1985), no. 1, 44–80. MR 772471, DOI 10.1016/0021-8693(85)90145-0
- Roberto Minio, An interview with Michael Atiyah, Math. Intelligencer 6 (1984), no. 1, 9–19. MR 735359, DOI 10.1007/BF03024202
- Bernd Baumann, Endliche Gruppen mit einer $2$-zentralen Involution, deren Zentralisator $2$-abgeschlossen ist, Illinois J. Math. 22 (1978), no. 2, 240–261 (German). MR 490825
- G. V. Belyĭ, Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 2, 267–276, 479 (Russian). MR 534593
- Helmut Bender, Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläßt, J. Algebra 17 (1971), 527–554 (German). MR 288172, DOI 10.1016/0021-8693(71)90008-1
- Helmut Bender, On groups with abelian Sylow $2$-subgroups, Math. Z. 117 (1970), 164–176. MR 288180, DOI 10.1007/BF01109839
- Helmut Bender, On the uniqueness theorem, Illinois J. Math. 14 (1970), 376–384. MR 262351
- Helmut Bender, Goldschmidt’s $2$-signalizer functor theorem, Israel J. Math. 22 (1975), no. 3-4, 208–213. MR 390056, DOI 10.1007/BF02761590
- Helmut Bender and George Glauberman, Characters of finite groups with dihedral Sylow $2$-subgroups, J. Algebra 70 (1981), no. 1, 200–215. MR 618388, DOI 10.1016/0021-8693(81)90253-2
- Robert J. Blattner, Induced and produced representations of Lie algebras, Trans. Amer. Math. Soc. 144 (1969), 457–474. MR 308223, DOI 10.1090/S0002-9947-1969-0308223-4
- Richard E. Block and Robert Lee Wilson, The restricted simple Lie algebras are of classical or Cartan type, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), no. 16, , Phys. Sci., 5271–5274. MR 758423, DOI 10.1073/pnas.81.16.5271
- Enrico Bombieri, A. Odlyzko, and D. Hunt, Thompson’s problem $(\sigma ^{2}=3)$, Invent. Math. 58 (1980), no. 1, 77–100. Appendices by A. Odlyzko and D. Hunt. MR 570875, DOI 10.1007/BF01402275
- A. Borel and J. Tits, Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I, Invent. Math. 12 (1971), 95–104 (French). MR 294349, DOI 10.1007/BF01404653
- 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. MR 0095203
- Richard Brauer, Some applications of the theory of blocks of characters of finite groups. II, J. Algebra 1 (1964), 307–334. MR 174636, DOI 10.1016/0021-8693(64)90011-0
- Richard Brauer and K. A. Fowler, On groups of even order, Ann. of Math. (2) 62 (1955), 565–583. MR 74414, DOI 10.2307/1970080
- 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. MR 109846, DOI 10.1073/pnas.45.12.1757
- Francis Buekenhout, Diagrams for geometries and groups, J. Combin. Theory Ser. A 27 (1979), no. 2, 121–151. MR 542524, DOI 10.1016/0097-3165(79)90041-4 39. P. Cameron, S. Praeger, J. Saxl, and G. Seitz, The Sims conjecture (to appear).
- G. Cherlin, L. Harrington, and A. H. Lachlan, $\aleph _0$-categorical, $\aleph _0$-stable structures, Ann. Pure Appl. Logic 28 (1985), no. 2, 103–135. MR 779159, DOI 10.1016/0168-0072(85)90023-5
- G. Cherlin and A. H. Lachlan, Stable finitely homogeneous structures, Trans. Amer. Math. Soc. 296 (1986), no. 2, 815–850. MR 846608, DOI 10.1090/S0002-9947-1986-0846608-8
- C. Chevalley, Sur certains groupes simples, Tohoku Math. J. (2) 7 (1955), 14–66 (French). MR 73602, DOI 10.2748/tmj/1178245104
- J. H. Conway, A characterisation of Leech’s lattice, Invent. Math. 7 (1969), 137–142. MR 245518, DOI 10.1007/BF01389796
- J. H. Conway and S. P. Norton, Monstrous moonshine, Bull. London Math. Soc. 11 (1979), no. 3, 308–339. MR 554399, DOI 10.1112/blms/11.3.308
- Charles W. Curtis, Central extensions of groups of Lie type, J. Reine Angew. Math. 220 (1965), 174–185. MR 188299, DOI 10.1515/crll.1965.220.174 46. A. Delgado and B. Stellmacher, Weak BN-pairs of rank2 (preprint).
- E. B. Dynkin, Maximal subgroups of the classical groups, Trudy Moskov. Mat. Obšč. 1 (1952), 39–166 (Russian). MR 0049903
- E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Mat. Sbornik N.S. 30(72) (1952), 349–462 (3 plates) (Russian). MR 0047629
- Freeman J. Dyson, Unfashionable pursuits, Math. Intelligencer 5 (1983), no. 3, 47–54. MR 737690, DOI 10.1007/BF03026573
- Michel Enguehard, Caractérisation des groupes de Ree, Astérisque 142-143 (1986), 49–139, 296 (French, with English summary). Révision dans les groupes finis. Groupes du type de Lie de rang $1$. MR 873958
- Burton Fein, William M. Kantor, and Murray Schacher, Relative Brauer groups. II, J. Reine Angew. Math. 328 (1981), 39–57. MR 636194, DOI 10.1515/crll.1981.328.39
- W. Feit, Rigidity of $\textrm {Aut}(\textrm {PSL}_2(p^2))$, $p\equiv \pm 2$ $(\textrm {mod}\,5),\;p\not = 2$, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 351–356. MR 817268
- J. G. Thompson, Rational rigidity of $G_2(5)$, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 321–322. MR 817265
- W. Feit, P. Fong, and B. Srinivasan, Rigidity of $\textrm {SL}_n(q)$ and certain subgroups for $(n,q-1)=1$ and $n>2$, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 303–307. MR 817263
- Walter Feit and John G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775–1029. MR 166261
- Bernd Fischer, Finite groups generated by $3$-transpositions. I, Invent. Math. 13 (1971), 232–246. MR 294487, DOI 10.1007/BF01404633
- Paul Fong, Characters arising in the Monster-modular connection, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 557–559. MR 604633
- Richard Foote, Aschbacher blocks, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 37–42. MR 604554
- I. B. Frenkel, J. Lepowsky, and A. Meurman, A natural representation of the Fischer-Griess Monster with the modular function $J$ as character, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), no. 10, , Phys. Sci., 3256–3260. MR 747596, DOI 10.1073/pnas.81.10.3256
- Robert Gilman, Components of finite groups, Comm. Algebra 4 (1976), no. 12, 1133–1198. MR 430053, DOI 10.1080/00927877608822156
- Robert H. Gilman and Robert L. Griess Jr., Finite groups with standard components of Lie type over fields of characteristic two, J. Algebra 80 (1983), no. 2, 383–516. MR 691810, DOI 10.1016/0021-8693(83)90007-8
- George Glauberman, Central elements in core-free groups, J. Algebra 4 (1966), 403–420. MR 202822, DOI 10.1016/0021-8693(66)90030-5
- George Glauberman, On solvable signalizer functors in finite groups, Proc. London Math. Soc. (3) 33 (1976), no. 1, 1–27. MR 417284, DOI 10.1112/plms/s3-33.1.1
- G. Glauberman, Factorizations in local subgroups of finite groups, Regional Conference Series in Mathematics, No. 33, American Mathematical Society, Providence, R.I., 1977. MR 0470072, DOI 10.1090/cbms/033 65. G. Glauberman, Local analysis in the odd order paper, Proc Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, p. 137.
- George Glauberman and Richard Niles, A pair of characteristic subgroups for pushing-up in finite groups, Proc. London Math. Soc. (3) 46 (1983), no. 3, 411–453. MR 699096, DOI 10.1112/plms/s3-46.3.411
- David M. Goldschmidt, Solvable signalizer functors on finite groups, J. Algebra 21 (1972), 137–148. MR 297861, DOI 10.1016/0021-8693(72)90040-3
- David M. Goldschmidt, $2$-signalizer functors on finite groups, J. Algebra 21 (1972), 321–340. MR 323904, DOI 10.1016/0021-8693(72)90027-0
- David M. Goldschmidt, $2$-fusion in finite groups, Ann. of Math. (2) 99 (1974), 70–117. MR 335627, DOI 10.2307/1971014
- David M. Goldschmidt, Strongly closed $2$-subgroups of finite groups, Ann. of Math. (2) 102 (1975), no. 3, 475–489. MR 393223, DOI 10.2307/1971040
- David M. Goldschmidt, Automorphisms of trivalent graphs, Ann. of Math. (2) 111 (1980), no. 2, 377–406. MR 569075, DOI 10.2307/1971203
- David M. Goldschmidt, Lectures on character theory, Publish or Perish, Inc., Wilmington, Del., 1980. MR 575526
- Daniel Gorenstein, On the centralizers of involutions in finite groups, J. Algebra 11 (1969), 243–277. MR 240188, DOI 10.1016/0021-8693(69)90056-8
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Daniel Gorenstein, The classification of finite simple groups. I. Simple groups and local analysis, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 1, 43–199. MR 513750, DOI 10.1090/S0273-0979-1979-14551-8
- Daniel Gorenstein, Finite simple groups, University Series in Mathematics, Plenum Publishing Corp., New York, 1982. An introduction to their classification. MR 698782, DOI 10.1007/978-1-4684-8497-7
- Daniel Gorenstein, The classification of finite simple groups. Vol. 1, The University Series in Mathematics, Plenum Press, New York, 1983. Groups of noncharacteristic $2$ type. MR 746470, DOI 10.1007/978-1-4613-3685-3
- Daniel Gorenstein and Koichiro Harada, Finite groups whose $2$-subgroups are generated by at most $4$ elements, Memoirs of the American Mathematical Society, No. 147, American Mathematical Society, Providence, R.I., 1974. MR 0367048
- Daniel Gorenstein and Richard Lyons, Nonsolvable finite groups with solvable $2$-local subgroups, J. Algebra 38 (1976), no. 2, 453–522. MR 407128, DOI 10.1016/0021-8693(76)90233-7
- Daniel Gorenstein and Richard Lyons, The local structure of finite groups of characteristic $2$ type, Mem. Amer. Math. Soc. 42 (1983), no. 276, vii+731. MR 690900, DOI 10.1090/memo/0276
- Daniel Gorenstein and John H. Walter, On the maximal subgroups of finite simple groups, J. Algebra 1 (1964), 168–213. MR 172917, DOI 10.1016/0021-8693(64)90032-8
- Daniel Gorenstein and John H. Walter, The characterization of finite groups with dihedral Sylow $2$-subgroups. I, J. Algebra 2 (1965), 85–151. MR 177032, DOI 10.1016/0021-8693(65)90027-X
- Daniel Gorenstein and John H. Walter, Centralizers of involutions in balanced groups, J. Algebra 20 (1972), 284–319. MR 292927, DOI 10.1016/0021-8693(72)90060-9
- Daniel Gorenstein and John H. Walter, Balance and generation in finite groups, J. Algebra 33 (1975), 224–287. MR 357583, DOI 10.1016/0021-8693(75)90123-4
- Robert L. Griess Jr., The friendly giant, Invent. Math. 69 (1982), no. 1, 1–102. MR 671653, DOI 10.1007/BF01389186
- Graham Higman, Suzuki $2$-groups, Illinois J. Math. 7 (1963), 79–96. MR 143815 87. G. Hoyden, Realisierung der Jankogrouppen J1 and J, Algebra J. (to appear). 88. G. Hoyden and B. Matzat, Realisierung sporadischer einfacher gruppen als Galoisgruppen ober Kreisteilungskorpern (to appear).
- David C. Hunt, Rational rigidity and the sporadic groups, J. Algebra 99 (1986), no. 2, 577–592. MR 837564, DOI 10.1016/0021-8693(86)90047-5
- I. Martin Isaacs, Character theory of finite groups, Pure and Applied Mathematics, No. 69, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0460423
- Zvonimir Janko, A new finite simple group of order $86\cdot 775\cdot 571\cdot 046\cdot 077\cdot 562\cdot 880$ which possesses $M_{24}$ and the full covering group of $M_{22}$ as subgroups, J. Algebra 42 (1976), no. 2, 564–596. MR 432751, DOI 10.1016/0021-8693(76)90115-0
- Zvonimir Janko, Nonsolvable finite groups all of whose $2$-local subgroups are solvable. I, J. Algebra 21 (1972), 458–517. MR 357584, DOI 10.1016/0021-8693(72)90009-9
- V. G. Kac, The classification of the simple Lie algebras over a field with non-zero characteristic, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 385–408 (Russian). MR 0276286
- V. G. Kac, A description of the filtered Lie algebras with which graded Lie algebras of Cartan type are associated, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 800–834 (Russian). MR 0369452 95. W. Kantor, Polynomial-time algorithms for finding elements of prime order and Sylow subgroups (submitted).
- Kenneth Klinger and Geoffrey Mason, Centralizers of $p$-groups in groups of characteristic $2$, $p$-type, J. Algebra 37 (1975), no. 2, 362–375. MR 390047, DOI 10.1016/0021-8693(75)90084-8
- A. I. Kostrikin and I. R. Šafarevič, Graded Lie algebras of finite characteristic, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 251–322 (Russian). MR 0252460
- John Leech, Some sphere packings in higher space, Canadian J. Math. 16 (1964), 657–682. MR 167901, DOI 10.4153/CJM-1964-065-1
- John Leech, Notes on sphere packings, Canadian J. Math. 19 (1967), 251–267. MR 209983, DOI 10.4153/CJM-1967-017-0
- Eugene M. Luks, Isomorphism of graphs of bounded valence can be tested in polynomial time, J. Comput. System Sci. 25 (1982), no. 1, 42–65. MR 685360, DOI 10.1016/0022-0000(82)90009-5
- J. Richard Lundgren, On finite simple groups all of whose $2$-local subgroups are solvable, J. Algebra 27 (1973), 491–515. MR 332953, DOI 10.1016/0021-8693(73)90060-4
- Richard Lyons, A characterization of the group $\textrm {U}_{3}\,(4)$, Trans. Amer. Math. Soc. 164 (1972), 371–387. MR 286881, DOI 10.1090/S0002-9947-1972-0286881-0
- Anne R. MacWilliams, On $2$-groups with no normal abelian subgroups of rank $3$, and their occurrence as Sylow $2$-subgroups of finite simple groups, Trans. Amer. Math. Soc. 150 (1970), 345–408. MR 276324, DOI 10.1090/S0002-9947-1970-0276324-3 104. G. Mason, The classification of quasithin simple groups (preprint).
- G. Mason, Modular forms and the theory of Thompson series, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 391–407. MR 817271
- B. Heinrich Matzat, Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht abelschem Kern, Invent. Math. 80 (1985), no. 2, 365–374 (German). MR 788415, DOI 10.1007/BF01388611 107. B. Matzat and A. Zeh, Realisierung der mathieugruppen M. Number Theory (to appear).
- Patrick Paschal McBride, Near solvable signalizer functors on finite groups, J. Algebra 78 (1982), no. 1, 181–214. MR 677717, DOI 10.1016/0021-8693(82)90107-7
- Emmy Noether, Gleichungen mit vorgeschriebener Gruppe, Math. Ann. 78 (1917), no. 1, 221–229 (German). MR 1511893, DOI 10.1007/BF01457099
- Thomas Peterfalvi, Le théorème de Bender-Suzuki. I, II, Astérisque 142-143 (1986), 141–233, 235–295, 296 (French, with English summary). Révision dans les groupes finis. Groupes du type de Lie de rang $1$. MR 873959
- Kok-wee Phan, On groups generated by three-dimensional special unitary groups. II, J. Austral. Math. Soc. Ser. A 23 (1977), no. 2, 129–146. MR 447427, DOI 10.1017/s1446788700018140
- Rimhak Ree, A family of simple groups associated with the simple Lie algebra of type $(F_{4})$, Amer. J. Math. 83 (1961), 401–420. MR 132781, DOI 10.2307/2372886
- Rimhak Ree, A family of simple groups associated with the simple Lie algebra of type $(G_{2})$, Amer. J. Math. 83 (1961), 432–462. MR 138680, DOI 10.2307/2372888
- M. A. Ronan and S. D. Smith, $2$-local geometries for some sporadic groups, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 283–289. MR 604595
- Gary M. Seitz, The root subgroups for maximal tori in finite groups of Lie type, Pacific J. Math. 106 (1983), no. 1, 153–244. MR 694680, DOI 10.2140/pjm.1983.106.153
- G. M. Seitz, Overgroups of irreducible linear groups, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 95–106. MR 817240
- I. R. Šafarevič, Construction of fields of algebraic numbers with given solvable Galois group, Izv. Akad. Nauk SSSR. Ser. Mat. 18 (1954), 525–578 (Russian). MR 0071469 118. D. Sibley, Groups of odd order revisited (in preparation).
- Charles C. Sims, Graphs and finite permutation groups, Math. Z. 95 (1967), 76–86. MR 204509, DOI 10.1007/BF01117534
- Charles C. Sims, Some group-theoretic algorithms, Topics in algebra (Proc. 18th Summer Res. Inst., Austral. Math. Soc., Austral. Nat. Univ., Canberra, 1978) Lecture Notes in Math., vol. 697, Springer, Berlin, 1978, pp. 108–124. MR 524367
- Fredrick Smith, Finite simple groups all of whose $2$-local subgroups are solvable, J. Algebra 34 (1975), 481–520. MR 376847, DOI 10.1016/0021-8693(75)90171-4
- Stephen D. Smith, Large extraspecial subgroups of widths $4$ and $6$, J. Algebra 58 (1979), no. 2, 251–281. MR 540638, DOI 10.1016/0021-8693(79)90160-1
- Stephen D. Smith, A characterization of orthogonal groups over $\textrm {GF}(2)$, J. Algebra 62 (1980), no. 1, 39–60. MR 561116, DOI 10.1016/0021-8693(80)90204-5
- Stephen D. Smith, A characterization of finite Chevalley and twisted groups of type $E$ over $\textrm {GF}(2)$, J. Algebra 62 (1980), no. 1, 101–117. MR 561119, DOI 10.1016/0021-8693(80)90207-0
- Stephen D. Smith, On the head characters of the Monster simple group, Finite groups—coming of age (Montreal, Que., 1982) Contemp. Math., vol. 45, Amer. Math. Soc., Providence, RI, 1985, pp. 303–313. MR 822245, DOI 10.1090/conm/045/822245
- Robert Steinberg, Variations on a theme of Chevalley, Pacific J. Math. 9 (1959), 875–891. MR 109191, DOI 10.2140/pjm.1959.9.875
- Robert Steinberg, Générateurs, relations et revêtements de groupes algébriques, Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962) Librairie Universitaire, Louvain; Gauthier-Villars, Paris, 1962, pp. 113–127 (French). MR 0153677
- Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335
- Robert Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. MR 0230728 130. G. Stroth, Solvable uniqueness subgroups (to appear).
- Michio Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc. 99 (1961), 425–470. MR 131459, DOI 10.1090/S0002-9947-1961-0131459-5
- Michio Suzuki, On a class of doubly transitive groups, Ann. of Math. (2) 75 (1962), 105–145. MR 136646, DOI 10.2307/1970423
- Michio Suzuki, On characterizations of linear groups. III, Nagoya Math. J. 21 (1962), 159–183. MR 142665, DOI 10.1017/S0027763000023813
- John G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable. II, Pacific J. Math. 33 (1970), 451–536. MR 276325, DOI 10.2140/pjm.1970.33.451 135. J. Thompson, Toward a characterization of E. I, II, III, J. Algebra 7 (1967), 406-414; 20 (1972), 610-621; 49 (1977), 163-166.
- J. G. Thompson, Some numerology between the Fischer-Griess Monster and the elliptic modular function, Bull. London Math. Soc. 11 (1979), no. 3, 352–353. MR 554402, DOI 10.1112/blms/11.3.352 137. J. Thompson, Some finite groups which appear as $\textrm {Gal}\,L/K$, where $K\subseteq Q(µ\sbn )$, J. Algebra 89 (1984), 437-499.
- John G. Thompson, Galois groups, Groups—St. Andrews 1989, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 160, Cambridge Univ. Press, Cambridge, 1991, pp. 455–462. MR 1123999, DOI 10.1017/CBO9780511661846.018
- J. G. Thompson, Rational rigidity of $G_2(5)$, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 321–322. MR 817265
- J. G. Thompson, Primitive roots and rigidity, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 327–350. MR 817267
- F. G. Timmesfeld, Groups generated by root-involutions. I, II, J. Algebra 33 (1975), 75–134; ibid. 35 (1975), 367–441. MR 372019, DOI 10.1016/0021-8693(75)90133-7
- Franz Timmesfeld, Finite simple groups in which the generalized Fitting group of the centralizer of some involution is extraspecial, Ann. of Math. (2) 107 (1978), no. 2, 297–369. MR 486255, DOI 10.2307/1971146 143. F. Timmesfeld, Tits geometries and parabolic systems in finite groups. I, II, Math. Z. 184 (1983), 377-396; 449-487.
- J. Tits, Algebraic and abstract simple groups, Ann. of Math. (2) 80 (1964), 313–329. MR 164968, DOI 10.2307/1970394
- Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099
- J. Tits, A local approach to buildings, The geometric vein, Springer, New York-Berlin, 1981, pp. 519–547. MR 661801 147. J. Tits, Affine buildings of rank $\geqslant 4$ (unpublished).
- W. T. Tutte, A family of cubical graphs, Proc. Cambridge Philos. Soc. 43 (1947), 459–474. MR 21678, DOI 10.1017/s0305004100023720
- W. T. Tutte, On the symmetry of cubic graphs, Canadian J. Math. 11 (1959), 621–624. MR 109794, DOI 10.4153/CJM-1959-057-2
- John H. Walter, The characterization of finite groups with abelian Sylow $2$-subgroups, Ann. of Math. (2) 89 (1969), 405–514. MR 249504, DOI 10.2307/1970648
- J. H. Walter, Classical groups as Galois groups, Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick, N.J., 1983–1984) Cambridge Univ. Press, Cambridge, 1985, pp. 357–383. MR 817269
- John H. Walter, The $B$-conjecture: $2$-components in finite simple groups, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 57–66. MR 604557
- Warren J. Wong, Determination of a class of primitive permutation groups, Math. Z. 99 (1967), 235–246. MR 214653, DOI 10.1007/BF01112454
- B. I. Zil′ber, Strongly minimal countably categorical theories, Sibirsk. Mat. Zh. 21 (1980), no. 2, 98–112, 237 (Russian). MR 569179
- Thomas Peterfalvi, Simplification du chapitre VI de l’article de Feit et Thompson sur les groupes d’ordre impair, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 12, 531–534 (French, with English summary). MR 770439
Additional Information
- Journal: Bull. Amer. Math. Soc. 14 (1986), 1-98
- MSC (1985): Primary 20D05, 20-02
- DOI: https://doi.org/10.1090/S0273-0979-1986-15392-9
- MathSciNet review: 818060