|
Blocks of characters and structure of finite groups
Author(s):
Richard
Brauer
Journal:
Bull. Amer. Math. Soc.
1
(1979),
21-38.
MSC (1970):
Primary 20C20
MathSciNet review:
513748
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [A] L. E. Dickson, Linear groups, B. G. Teubner, Leipzig, 1901.
- [B] Larry Dornhoff, Group representation theory in two parts:Part A. Ordinary representation theory. Part B. Modular representation theory, Marcel Dekker, Inc., New York, 1971-1972.
- [C] Bertram Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin, Heidelberg, New York, 1967. MR 224703
- [D] Daniel Gorenstein, Finite groups, Harper and Row, New York, Evanston, and London, 1968. MR 231903
- [E] I. Martin Isaacs, Character theory of finite groups, Academic Press, New York, San Francisco, London, 1976. MR 460423
- [F] Camille Jordan, Traité des substitutions et des équations algébriques, Gauthier-Villars, Paris, 1870.
- [G] Jean-Pierre Serre, Représentations linéaires des groupes finis, 2ieme éd., Hermann, Paris, 1971. MR 352231
- [H] Roger Carter, Simple groups and simple Lie algebras, J. London Math. Soc. 40 (1965), 193-240. MR 174655
- [I] Constance Davis, A bibliographical survey of simple groups of finite order, 1900-1965, Courant Institute, New York University, New York, 1969. MR 248203
- [J] Walter Feit, Representations of finite groups, Yale Lecture Notes, Part 1, 1969. Part II, 1975.
- [K] Walter Feit, The current situation in the theory of finite simple groups, Actes, Congres Intern. Math., 1970 Tome 1, p. 55 à 93. MR 427449
- [L] Daniel Gorenstein, Finite simple groups and their classification, Israel J. Math. 19 (1974), 5-66. MR 360797
- [M] James E. Humphreys, Ordinary and modular representations of Chevalley groups, Lecture Notes in Math., vol. 528, Springer-Verlag, Berlin and New York, 1976. MR 453884
- [N] Robert Steinberg, Lectures on Chevalley groups, Yale Lecture Notes, 1967. MR 466335
- [O] Seminar on algebraic groups and related finite groups, Lecture Notes in Math., vol. 131, Springer-Verlag, Berlin and New York, 1970.
- [P] Jacques Tits, Groupes simples et géométries associées, Internat. Congr. Math. 1962, 197-221. MR 175903
- [Q] Proceedings of the Second International Conference on the Theory of Groups, Lecture Notes in Math., vol. 372, Springer-Verlag, Berlin and New York, 1974.
- [R] Finite simple groups, Instructional Conference of the London Math. Soc. Academic Press, London and New York, 1971 MR 327886
- [S] Proceedings of the Conference on Finite Groups in Park City, Utah, 1975, Academic Press, New York, San Francisco, and London, 1976.
- 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.
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1970):
20C20
Retrieve articles in all Journals with MSC
(1970):
20C20
Additional Information:
DOI:
10.1090/S0273-0979-1979-14548-8
PII:
S 0273-0979(1979)14548-8
|