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Bulletin of the American Mathematical Society

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Blocks of characters and structure of finite groups


Author: Richard Brauer
Journal: Bull. Amer. Math. Soc. 1 (1979), 21-38
MSC (1970): Primary 20C20
DOI: https://doi.org/10.1090/S0273-0979-1979-14548-8
MathSciNet review: 513748
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  • 1. J. L. Alperin, The main problem of block theory, [S] (1976), 341-356. MR 404417
  • 2. 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
  • 3. J. L. Alperin, Finite simple groups of 2-rank two, Scripta Math. 29 (1973), 195-214. MR 401902
  • 4. H. F. Blichfeldt, Finite collineation groups, Univ. of Chicago Press, Chicago, Ill., 1917.
  • 5. Richard Brauer, On groups whose order contains a prime to the first order. I, Amer. J. Math. 64 (1942), 401-420; II, Amer. J. Math. 64 (1942), 421-440.
  • 6. Richard Brauer, On permutation groups of prime degree and related groups, Ann. of Math. 44 (1943), 57-79. MR 8237
  • 7. Richard Brauer, On the structure of groups of finite order, Proc. Internat Congr. Math., Amsterdam, 1954, vol. 1, 209-217. MR 95203
  • 8. Richard Brauer, Zur Darstellungstheorie der Gruppen endlicher Ordnung. I, Math. Z. 63 (1956), 406-444; II, Math. Z. 72 (1959), 25-46. MR 75953
  • 9. Richard Brauer, Some applications of the theory of blocks, I, J. Algebra 1 (1964), 152-167; II, J. Algebra 1 (1964), 307-334; III, J. Algebra 3 (1966), 225-255; IV, J. Algebra 17 (1971), 481-529; V. J. Algebra 28 (1974), 433-440.
  • 10. Richard Brauer, On blocks and sections infinite groups. I, Amer. J. Math. 89 (1967), 1115-1136; II, Amer. J. Math. 90 (1968), 895-925.
  • 11. Richard Brauer, Über endliche Gruppen von Primzahlgrad, Math. Ann. 169 (1967), 73-96. MR 206088
  • 12. Richard Brauer, On simple groups of order, 5 3 2, Bull. Amer. Math. Soc. 74 (1968), 900-903. MR 236255
  • 13. Richard Brauer, On the order of finite projective groups in a given dimension, Nachr. Akad. Wiss. Göttingen Math.-Phys. K1 II, 1969. MR 246979
  • 14. Richard Brauer, On the structure of blocks of characters of finite groups, [Q] (1973), 103-130. MR 352238
  • 15. Richard Brauer, On finite groups with a cyclic Sylow subgroup. I, J. Algebra 40 (1976), 556-584. MR 417271
  • 16. Richard Brauer and Walter Feit, On the number of irreducible characters of finite groups in a given block, Proc. Nat Acad. Sci. U.S.A. 45 (1959), 361-365. MR 106246
  • 17. Richard Brauer and Walter Feit, An analogue of Jordan's theorem in characteristic p, Ann. of Math. (2) 84 (1966), 381-399. MR 200350
  • 18. Richard Brauer and Paul Fong, A characterization of the Mathieu group M, Trans. Amer. Math. Soc. 122 (1966), 18-47. MR 207817
  • 19. Richard Brauer and Paul Fong, On the centralizers of p-elements infinite groups, Bull. London Math. Soc. 6 (1974), 319-324. MR 357580
  • 20. Richard Brauer and W. F. Reynolds, On a problem of E. Artin, Ann. of Math. (2) 68 (1958), 713-720. MR 100635
  • 21. Richard Brauer and Michio Suzuki, On finite groups whose 2-Sylow group is a quaternion group, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1888-1891. MR 133374
  • 22. Richard Brauer and H. F. Tuan, On simple groups of finite order, Bull. Amer. Math. Soc. 51 (1945), 756-766. MR 15102
  • 23. Michel Broué, Radical, hauteur, p-sections et blocs, Ann. of Math. (2) 107 (1978), 89-107. MR 485862
  • 24. W. Burnside, The theory of groups of finite order, 2nd ed., Cambridge Univ. Press, 1911.
  • 25. Claude Chevalley, Sur certains groupes simples, Tôhoku Math. J. (2) 7 (1955), 14-66. MR 73602
  • 26. Michael Collins, A characterization of the Suzuki groups by their Sylow 2-subgroups, Math. Z. 123 (1971), 32-48. MR 308252
  • 27. Michael Collins, The characterization of the unitary groups U3(2n) by their Sylow 2-subgroups, Bull, London Math. Soc. 4 (1972), 49-53. MR 340441
  • 28. E. C. Dade, Blocks with cyclic defect groups, Ann. of Math. (2) 84 (1966), 20-48. MR 200355
  • 29. L. E. Dickson, Theory of linear groups in an arbitrary field, Trans. Amer. Math. Soc. 2 (1901), 363-394. MR 1500573
  • 30. L. E. Dickson, A new system of simple groups, Math. Ann. 60 (1905), 137-150. MR 1511290
  • 31. Walter Feit, Groups which have a faithful representation of degree less than p - 1, Trans. Amer. Math. Soc. 112 (1964), 287-303. MR 161906
  • 32. Walter Feit, On finite linear groups in dimension at most 10, in[S] (1976), 397-407. MR 412294
  • 33. Walter Feit and John G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775-1029. MR 166261
  • 34. Paul Fong, Sylow 2-subgroups of small order (unpublished).
  • 35. Paul Fong and W. J. Wong, A characterization of the finite simple groups PSp(4, p), G2(q), D4(2)(q). I, Nagoya Math. J. 36 (1969), 143-184; II, Nagoya Math. J. 39 (1976), 39-79. MR 255666
  • 36. F. J. Fuglister, On a problem of E. Artin, Ph.D. thesis, Harvard University, 1974.
  • 37. Daniel Gorenstein, On finite simple groups of characteristic 2-type, Publ. Math. Inst. Hautes Études Sci., No. 36, 1969. MR 260864
  • 38. Daniel Gorenstein and John Walter, The characterization of finite groups with dihedral Sylow 2-subgroups. I, J. Algebra 2 (1965), 85-151. MR 177032
  • 39. J. A, Green, On the indecomposable representations of a finite group, Math. Z. 70 (1958), 430-445. MR 131454
  • 40. J. A, Green, Blocks of modular representations, Math. Z. 79 (1962), 100-115. MR 141717
  • 41. J. A, Green, A transfer theorem for modular representations, J. Algebra 1 (1964), 73-84. MR 162843
  • 42. Marshall Hall, Jr., A search for simple groups of order less than one million, Computational Problems in Abstract Algebra, Pergamon Press, New York, 1969, 137-168. MR 272887
  • 43. Marshall Hall, Jr., Simple groups of order less than one million, J. Algebra 20 (1972), 98-102. MR 285603
  • 44. Marcel Herzog, On a problem of E. Artin, J. Algebra 15 (1970), 408-416. MR 260862
  • 45. W. C. Huffman and D. B. Wales, Linear groups of degree eight with no elements of order seven, Illinois J. Math. 20 (1976), 519-527. MR 409678
  • 46. Noboru Ito, Frobenius and Zassenhaus groups, Lecture Notes, University of Illinois at Chicago Circle, 1968-1969.
  • 47. Zvinomir Janko, A new finite simple group with abelian Sylow 2-subgroup and its characterization, J. Algebra 3 (1966), 147-186. MR 193138
  • 48. Zvinomir Janko, Some new simple groups of finite order, Symposia Mathematica, vol. 1, 25-46. Academic Press, London, 1969. MR 244371
  • 49. Kenneth Klinger, Finite groups of order 2313, J. Algebra 41 (1976), 303-326. MR 414689
  • 50. Peter Landrock, On elementary abelian and dihedral defect groups, Ph.D. Thesis, University of Chicago, 1974.
  • 51. J. S. Leon and David Wales, Simple groups of order 23p, J. Algebra 29 (1974), 246-254. MR 338153
  • 52. J. H. Lindsay, II, Finite linear groups of degree six, Canad. J. Math. 23 (1971), 171-190. MR 289665
  • 53. Geoffrey Mason, Finite groups of order 2317. I, J. Algebra 40 (1976), 309-339; II, J. Algebra 41 (1976), 327-346; III, J. Algebra 41 (1976), 347-364.
  • 54. Sister Elizabeth Louise Michaels, A study of simple groups of even order, Ph.D. Thesis, University of Notre Dame, 1963.
  • 55. J. B. Olsson, On 2-blocks with given defect groups, Ph.D. Thesis, University of Chicago, 1974.
  • 56. David Parrott, On the Mathieu groups M22 and M11, J. Austral. Math. Soc. 11 (1970), 69-81. MR 255669
  • 57. David Parrott and S. K. Wong, On the Higman-Sims simple group of order 44, 352, 000, Pacific J. Math. 32 (1970), 501-516. MR 257216
  • 58. Rimhak Ree, A family of simple groups associated with the simple Lie algebra of type F4, Amer. J. Math. 83 (1961), 401-420. MR 132781
  • 59. Rimhak Ree, A family of simple groups associated with the simple Lie algebra of type G2, Amer. J. Math. 83 (1961), 432-462. MR 138680
  • 60. Ronald Solomon, On defect groups and p-constraint, J. Algebra 31 (1974), 557-561. MR 422398
  • 61. R. G. Stanton, The Mathieu groups, Canad. J. Math. 3 (1951), 164-174. MR 40304
  • 62. Michio Suzuki, A new type of simple groups of finite order, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 868-870. MR 120283
  • 63. J. G. Thompson, Vertices and sources, J. Algebra 6 (1967), 1-7. MR 215906
  • 64. J. G. Thompson, Towards a characterization of E(q). I, J. Algebra 7 (1967), 406-414; II, J. Algebra 20 (1972), 610-621.
  • 65. J. G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable. I, Bull. Amer. Math. Soc. 74 (1968), 383-437; II-VI, Pacific J. Math. 33 (1970), 451-536; 39 (1971), 483-534, 48 (1973), 511-592; 50 (1974), 215-297; 51 (1974), 573-630. MR 230809
  • 66. H. F. Tuan, On simple groups of order less than10, 000 (unpublished).
  • 67. D. B. Wales, Finite linear groups of degree seven. I., Canad. J. Math. 21 (1969), 1042-1056; II, Canad. J. Math. 22 (1970), 207-235. MR 248237
  • 68. D. B. Wales, Simple groups of order 7 3 2, J. Algebra 16 (1970), 575-595. MR 268270
  • 69. H. N. Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc. 121 (1966), 62-89. MR 197587
  • 70. Hans Zassenhaus, Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen, Abh. Math. Sem. Univ. Hamburg 11 (1936), 17-40.

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DOI: https://doi.org/10.1090/S0273-0979-1979-14548-8

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