|
Galois theory on the line in nonzero characteristic
Author(s):
Shreeram
S.
Abhyankar
Journal:
Bull. Amer. Math. Soc.
27
(1992),
68-133.
MSC (1991):
Primary 12F10, 14H30, 20D06, 20E22
MathSciNet review:
1118002
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [A1]
- S. S. Abhyankar, On the ramification of algebraic functions, Amer. J. Math. \textbf{77} (1955), 572--592. MR 71851
- [A2]
- S. S. Abhyankar, Local uniformization on algebraic surfaces over ground fields of characteristic $p\ne 0$, Ann. of Math. \textbf{63} (1956), 491--526. MR 78017
- [A3]
- S. S. Abhyankar, Coverings of algebraic curves, Amer. J. Math. \textbf{79} (1957), 825--856. MR 94354
- [A4]
- S. S. Abhyankar, On the ramification of algebraic functions part {\rm II}\RM : Unaffected equations for characteristic two, Trans. Amer. Math. Soc. \textbf{89 \rm (1958) \year 1958}, 310--324. MR 98749
- [A5]
- S. S. Abhyankar, Tame coverings and fundamental groups of algebraic varieties, Part {\rm III:} Some other sets of conditions for the fundamental group to be abelian, Amer. J. Math. \textbf{82} (1960), 179--190. MR 110707
- [A6]
- S. S. Abhyankar, Algebraic geometry for scientists and engineers, Amer. Math. Soc., Providence, RI, 1990. MR 1075991
- [A7]
- S. S. Abhyankar, Square-root parametrization of plane curves \rm (to appear). MR 1272021
- [As]
- M. Aschbacher, Finite groups, Cambridge University Press, Cambridge, 1986. MR 895134
- [B]
- R. Brauer, On the structure of groups of finite order, Proc. Internat. Congress Math. \textbf{1} (1954), 209--217. MR 95203
- [Bu]
- W. Burnside, Theory of groups of finite order, Cambridge University Press, Cambridge, 1911. MR
- [BP]
- W. S. Burnside and A. W. Panton, Theory of equations, Vols. I and II, Dublin, Hodges, Figgs and Co., London, 1904. MR
- [C]
- P. J. Cameron, Finite permutation groups and finite simple groups, Bull. London Math. Soc. \textbf{13} (1981), 1--22. MR 599634
- [Ca]
- R. D. Carmichael, Groups of finite order, Dover, New York, 1956. MR 75938
- [Ch]
- C. Chevalley, Sur certains groupes simples, T\^ohoku Math. J. \textbf{7} (1955), 14--66. MR 73602
- [CKS]
- C. W. Curtis, W. M. Kantor, and G. M. Seitz, The \RM 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc. \textbf{218} (1976), 1--59. MR 422440
- [D1]
- L. E. Dickson, Linear groups with an exposition of the Galois field theory, Teubner, Leipzig, 1958. MR 104735
- [D2]
- L. E. Dickson, On finite algebras, Nachr. Akad. Wiss. G\"ottingen (1905), 358--393. MR
- [F]
- W. Feit, On a class of doubly transitive permutation groups, Illinois J. Math. \textbf{4} (1960), 170--186. MR 113953
- [Fr]
- F. G. Frobenius, \"Uber aufl\"osbare Gruppen \rm IV, Sitzungsberichte der K\"oniglich Preu\ss ischen Akademie der Wissenchaften zu Berlin (1901), 1216--1230; reprinted as No. 63 on pages 189-203 of Band III of the ``Gesammelte Abhandlungen'' of Frobenius published by Springer-Verlag, New York, 1968. MR
- [FT]
- W. Feit and J. Thompson, Solvability of groups of odd order, Pacific J. Math. \textbf{13} (1963), 775--1029. MR 166261
- [G1]
- D. Gorenstein, Finite groups, Chelsea Publishing Company, New York, 1980. MR 569209
- [G2]
- D. Gorenstein, Finite simple groups, Plenum Press, New York, 1983. MR 746470
- [G3]
- D. Gorenstein, Classifying the finite simple groups, Bull. Amer. Math. Soc. \textbf{14} (1986), 1--98. MR 818060
- [G4]
- D. Gorenstein, The classification of the finite simple groups, a personal journey\,\RM : The early years\,, {\rm A Century of Mathematics in America, Part I}, Hist. of Math., vol. 1, Amer. Math. Soc., Providence, RI, 1988, pp. 447--476. MR 1003189
- [H]
- D. Hilbert, \"Uber die Irreduzibilit\"at ganzzahligen Koefficienten, Crelle J. \textbf{110} (1892), 104--129. MR
- [HB]
- B. Huppert and N. Blackburn, Finite groups \rm I, II, III, Springer-Verlag, New York, 1982. MR
- [J1]
- C. Jordan, Trait\'e des substitutions et des \'equations alg\'ebriques, Gauthier-Vill., Paris, 1870. MR
- [J2]
- C. Jordan, Th\'eor\`emes sur les groupes primitifs, J. Math. Pures Appl. \textbf{16}, 383--408. MR
- [J3]
- C. Jordan, Sur la limite de transitivit\'e des groupes non altern\'es, Bull. Soc. Math. France \textbf{1 \year 1873}, 40--71. MR 1503635
- [K1]
- W. M. Kantor, Rank \RM 3 characterizations of classical geometries, J. Algebra \textbf{36} (1975), 309--313. MR 387386
- [K2]
- W. M. Kantor, Homogeneous designs and geometric lattices, J. Combin. Theory Ser. A \textbf{38} (1985), 66--74. MR 773556
- [KL]
- W. M. Kantor and R. L. Liebler, The rank \RM 3 permutation representations of the finite classical groups, Trans. Amer. Math. Soc. \textbf{271} (1982), 1--71. MR 648077
- [L]
- M. W. Liebeck, The affine permutation groups of rank three, Proc. London Math. Soc. \textbf{54} (1987), 477--516. MR 879395
- [Mar]
- B. Marggraff, \"Uber primitive Gruppen mit transitiven Untergruppen geringeren Grades, Dissertation, Giessen, 1892. MR
- [Mas]
- G. Mason, The classification of quasi-thin simple groups. \rm (To appear). MR
- [Mat]
- E. Mathieu, M\'emoire sur l'\'etude des fonctions de plusieurs quantit\'es, sur la mani\`ere de les former, et sur les substitutions qui les laissent invariables, J. Math Pures Appl., \textbf{18} (1861), 241--323. MR
- [Mo]
- E. H. Moore, International Mathematics Congress, Chicago \rm 1893, New York, 1896, p. 210. MR
- [N]
- P. M. Neumann, Some primitive permutation groups, Proc. London Math. Soc. \textbf{50} (1985), 265--281. MR 772713
- [O]
- M. E. O'Nan, Normal structure of the one-point stabilizer of a doubly transitive permutation group {\rm I} and {\rm II}, Trans. Amer. Math. Soc. \textbf{214} (1975), 1--74. MR 393207
- [R]
- R. Ree, Sur une famille de groupes de permutations doublement transitifs, Canad. J. Math. \textbf{16} (1964), 797--820. MR 175965
- [S1]
- J-P. Serre, G\'eom\'etrie alg\'ebrique et g\'eom\'etrie analytique, Ann. Inst. Fourier \textbf{6} (1956), 1--42. MR 82175
- [S2]
- J-P. Serre, Algebraic Groups and Class Fields, Springer-Verlag, New York, 1988. MR 918564
- [St]
- R. Steinberg, Variations on a theme of Chevalley, Pacific J. Math. \textbf{9} (1959), 875--891. MR 109191
- [Su1]
- M. Suzuki, On a class of doubly transitive groups, Ann. Math. \textbf{75} (1962), 104--145. MR 136646
- [Su2]
- M. Suzuki, Group Theory {\rm I, II}, Springer-Verlag, New York, 1986. MR 648772
- [V]
- B. L. van der Waerden, Modern Algebra \rm I, II, Frederick Ungar Publishing Co., New York, 1949. MR
- [W]
- J. H. M. Wedderburn, A theorem on finite algebras, Trans. Amer. Math. Soc. \textbf{6 \rm (1905)}, 349--352. MR 1500717
- [Wi]
- H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. MR 183775
- [Z1]
- H. Zassenhaus, Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen, Abh. Math. Sem. Univ. Hamburg \textbf{11} (1936), 17--44. MR
- [Z2]
- H. Zassenhaus, \"Uber endliche Fastk\"orper, Abh. Math. Sem. Univ. Hamburg \textbf{11 \year 1936}, 187--220. MR
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1991):
12F10, 14H30, 20D06, 20E22
Retrieve articles in all Journals with MSC
(1991):
12F10, 14H30, 20D06, 20E22
Additional Information:
DOI:
10.1090/S0273-0979-1992-00270-7
PII:
S 0273-0979(1992)00270-7
|