Galois Theory on the Line in Nonzero Characteristic

  title={Galois Theory on the Line in Nonzero Characteristic},
  author={Shreeram S. Abhyankar},
and let α1, . . . , αn be its roots, which are assumed to be distinct. By definition, the Galois Group G of this equation consists of those permutations of the roots which preserve all relations between them. Equivalently, G is the set of all those permutations σ of the symbols {1, 2, . . . , n} such that φ(ασ(1), . . . , ασ(n)) = 0 for every n-variable polynomial φ for which φ(α1, . . . , αn) = 0. The coefficients of φ are supposed to be in a field K which contains the coefficients a1… CONTINUE READING
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Über primitive Gruppen mit transitiven Untergruppen geringeren Grades

  • B. Marggraff
  • Dissertation, Giessen
  • 1892
Highly Influential
6 Excerpts

Traité des substitutions et des équations algébriques

  • C. Jordan
  • Gauthier-Vill., Paris
  • 1870
Highly Influential
9 Excerpts

Finite groups I

  • B. Huppert, N. Blackburn
  • II, III, Springer-Verlag, New York
  • 1982
Highly Influential
10 Excerpts

Linear groups with an exposition of the Galois field theory

  • L. E. Dickson
  • Teubner, Leipzig
  • 1958
Highly Influential
5 Excerpts

Some primitive permutation groups

  • P. M. Neumann
  • Proc. London Math. Soc
  • 1985

Finite groups

  • D. Gorenstein
  • Chelsea Publishing Company, New York
  • 1980

The 2-transitive permutation representations of the finite Chevalley groups

  • C. W. Curtis, W. M. Kantor, G. M. Seitz
  • Trans. Amer. Math. Soc
  • 1976

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