|
Galois theory on the line in nonzero characteristic
Author(s):
Shreeram S.
Abhyankar
Journal:
Bull. Amer. Math. Soc.
27
(1992),
68-133.
MSC (2000):
Primary 12F10;
Secondary 14H30, 20D06
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. 77 (1955), 572-592. MR 0071851 (17:193c)
- [A2]
- -, Local uniformization on algebraic surfaces over ground fields of characteristic
, Ann. of Math. 63 (1956), 491-526. MR 0078017 (17:1134d) - [A3]
- -, Coverings of algebraic curves, Amer. J. Math. 79 (1957), 825-856. MR 0094354 (20:872)
- [A4]
- -, On the ramification of algebraic functions part II: Unaffected equations for characteristic two, Trans. Amer. Math. Soc. 89 (1958), 310-324. MR 0098749 (20:5204)
- [A5]
- -, Tame coverings and fundamental groups of algebraic varieties, Part III: Some other sets of conditions for the fundamental group to be abelian, Amer. J. Math. 82 (1960), 179-190. MR 0110707 (22:1575)
- [A6]
- -, Algebraic geometry for scientists and engineers, Amer. Math. Soc., Providence, RI, 1990. MR 1075991 (92a:14001)
- [A7]
- -, Square-root parametrization of plane curves (to appear).
- [As]
- M. Aschbacher, Finite groups, Cambridge University Press, Cambridge, 1986. MR 895134 (89b:20001)
- [B]
- R. Brauer, On the structure of groups of finite order, Proc. Internat. Congress Math. 1 (1954), 209-217. MR 0095203 (20:1709)
- [Bu]
- W. Burnside, Theory of groups of finite order, Cambridge University Press, Cambridge, 1911.
- [BP]
- W. S. Burnside and A. W. Panton, Theory of equations, Vols. I and II, Dublin, Hodges, Figgs and Co., London, 1904.
- [C]
- P. J. Cameron, Finite permutation groups and finite simple groups, Bull. London Math. Soc. 13 (1981), 1-22. MR 599634 (83m:20008)
- [Ca]
- R. D. Carmichael, Groups of finite order, Dover, New York, 1956. MR 0075938 (17:823a)
- [Ch]
- C. Chevalley, Sur certains groupes simples, Tôhoku Math. J. 7 (1955), 14-66. MR 0073602 (17:457c)
- [CKS]
- C. W. Curtis, W. M. Kantor, and G. M. Seitz, The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc. 218 (1976), 1-59. MR 0422440 (54:10429)
- [D1]
- L. E. Dickson, Linear groups with an exposition of the Galois field theory, Teubner, Leipzig, 1958. MR 0104735 (21:3488)
- [D2]
- -, On finite algebras, Nachr. Akad. Wiss. Göttingen (1905), 358-393.
- [F]
- W. Feit, On a class of doubly transitive permutation groups, Illinois J. Math. 4 (1960), 170-186. MR 0113953 (22:4784)
- [Fr]
- F. G. Frobenius, Über auflösbare Gruppen IV, Sitzungsberichte der Königlich Preußischen 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.
- [FT]
- W. Feit and J. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775-1029. MR 0166261 (29:3538)
- [G1]
- D. Gorenstein, Finite groups, Chelsea Publishing Company, New York, 1980. MR 569209 (81b:20002)
- [G2]
- -, Finite simple groups, Plenum Press, New York, 1983.
- [G3]
- -, Classifying the finite simple groups, Bull. Amer. Math. Soc. 14 (1986), 1-98. MR 818060 (87k:20001)
- [G4]
- -, The classification of the finite simple groups, a personal journey: The early years, A Century of Mathematics in America, Part I, Hist. of Math., vol. 1, Amer. Math. Soc., Providence, RI, 1988, pp. 447-476. MR 1003189 (90g:01031)
- [H]
- D. Hilbert, Über die Irreduzibilität ganzzahligen Koefficienten, Crelle J. 110 (1892), 104-129.
- [HB]
- B. Huppert and N. Blackburn, Finite groups I, II, III, Springer-Verlag, New York, 1982.
- [J1]
- C. Jordan, Traité des substitutions et des équations algébriques, Gauthier-Vill., Paris, 1870.
- [J2]
- -, Théorèmes sur les groupes primitifs, J. Math. Pures Appl. 16, 383-408.
- [J3]
- -, Sur la limite de transitivité des groupes non alternés, Bull. Soc. Math. France 1, 40-71. MR 1503635
- [K1]
- W. M. Kantor, Rank 3 characterizations of classical geometries, J. Algebra 36 (1975), 309-313. MR 0387386 (52:8229)
- [K2]
- -, Homogeneous designs and geometric lattices, J. Combin. Theory Ser. A 38 (1985), 66-74. MR 773556 (87c:51007)
- [KL]
- W. M. Kantor and R. L. Liebler, The rank 3 permutation representations of the finite classical groups, Trans. Amer. Math. Soc. 271 (1982), 1-71. MR 648077 (84h:20040)
- [L]
- M. W. Liebeck, The affine permutation groups of rank three, Proc. London Math. Soc. 54 (1987), 477-516. MR 879395 (88m:20004)
- [Mar]
- B. Marggraff, Über primitive Gruppen mit transitiven Untergruppen geringeren Grades, Dissertation, Giessen, 1892.
- [Mas]
- G. Mason, The classification of quasi-thin simple groups. (To appear).
- [Mat]
- E. Mathieu, Mémoire sur l'étude des fonctions de plusieurs quantités, sur la manière de les former, et sur les substitutions qui les laissent invariables, J. Math Pures Appl., 18 (1861), 241-323.
- [Mo]
- E. H. Moore, International Mathematics Congress, Chicago 1893, New York, 1896, p. 210.
- [N]
- P. M. Neumann, Some primitive permutation groups, Proc. London Math. Soc. 50 (1985), 265-281. MR 772713 (86d:20005)
- [O]
- M. E. O'Nan, Normal structure of the one-point stabilizer of a doubly transitive permutation group I and II, Trans. Amer. Math. Soc. 214 (1975), 1-74. MR 0393207 (52:14017)
- [R]
- R. Ree, Sur une famille de groupes de permutations doublement transitifs, Canad. J. Math. 16 (1964), 797-820. MR 0175965 (31:241)
- [S1]
- J-P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier 6 (1956), 1-42. MR 0082175 (18:511a)
- [S2]
- -, Algebraic Groups and Class Fields, Springer-Verlag, New York, 1988. MR 918564 (88i:14041)
- [St]
- R. Steinberg, Variations on a theme of Chevalley, Pacific J. Math. 9 (1959), 875-891. MR 0109191 (22:79)
- [Su1]
- M. Suzuki, On a class of doubly transitive groups, Ann. Math. 75 (1962), 104-145. MR 0136646 (25:112)
- [Su2]
- -, Group Theory I, II, Springer-Verlag, New York, 1986.
- [V]
- B. L. van der Waerden, Modern Algebra I, II, Frederick Ungar Publishing Co., New York, 1949.
- [W]
- J. H. M. Wedderburn, A theorem on finite algebras, Trans. Amer. Math. Soc. 6 (1905), 349-352. MR 1500717
- [Wi]
- H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. MR 0183775 (32:1252)
- [Z1]
- H. Zassenhaus, Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen, Abh. Math. Sem. Univ. Hamburg 11 (1936), 17-44.
- [Z2]
- -, Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamburg 11, 187-220.
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(2000):
12F10, 14H30, 20D06
Retrieve articles in all Journals with MSC
(2000):
12F10, 14H30, 20D06
Additional Information:
DOI:
10.1090/S0273-0979-1992-00270-7
PII:
S 0273-0979(1992)00270-7
Copyright of article:
Copyright
1992,
American Mathematical Society
|