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Galois embeddings for linear groups


Author: Shreeram S. Abhyankar
Journal: Trans. Amer. Math. Soc. 352 (2000), 3881-3912
MSC (2000): Primary 12F10, 14H30, 20D06, 20E22
DOI: https://doi.org/10.1090/S0002-9947-00-02438-7
Published electronically: April 18, 2000
MathSciNet review: 1650057
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Abstract | References | Similar Articles | Additional Information

Abstract:

A criterion is given for the solvability of a central Galois embedding problem to go from a projective linear group covering to a vectorial linear group covering.


References [Enhancements On Off] (What's this?)

  • [Ab1] S. S. Abhyankar, Nice equations for nice groups, Israel Journal of Mathematics 88 (1994), 1-24. MR 96f:12003
  • [Ab2] S. S. Abhyankar, Projective polynomials, Proceedings of the American Mathematical Society 125 (1997), 1643-1650. MR 98a:12001
  • [Ab3] S. S. Abhyankar, Galois theory of semilinear transformations, London Math. Soc. Lecture Note Ser., 256, Cambridge Univ. Press, Cambridge, 1999. CMP 2000:01
  • [Art] E. Artin, Geometric Algebra, Interscience, 1957. MR 18:553e
  • [Car] R. W. Carter, Simple Groups of Lie Type, Wiley, 1977.
  • [Dem] P. Dembowski, Finite Geometries, Springer-Verlag, 1968. MR 97i:51005
  • [Di1] J. Dieudonné, On the Automorphisms of the Classical Groups, Memoirs of the American Mathematical Society No. 2, 1951. MR 13:531a
  • [Di2] J. Dieudonné, La Géométrie des Groupes Classiques, Springer-Verlag, 1955. MR 17:236a
  • [Hu1] L. K. Hua, On the automorphisms of the symplectic group over any field, Annals of Mathematics 49 (1948), 739-759. MR 10:352e
  • [Hu2] L. K. Hua, Supplement to Dieudonné's book On the Automorphisms of the Classical Groups, Memoirs of the American Mathematical Society No. 2, 1951, pp. 96-122. MR 82c:20079
  • [ScW] O. Schreier and B. L. van der Waerden, Die Automorphismen der projectiven Gruppen, Abhand. Math. Seminar Univ. Hamburg 6 (1928), 303-322.
  • [Ste] R. Steinberg, Automorphisms of finite linear groups, Canadian Journal of Mathematics 12 (1960), 606-615. MR 22:12165
  • [Suz] M. Suzuki, Group Theory I, Springer-Verlag, 1982. MR 82k:20001c
  • [VeY] O. Veblen and J. W. Young, Projective Geometry, Vols. I and II, Ginn and Company, 1910-1918.

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Additional Information

Shreeram S. Abhyankar
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: ram@cs.purdue.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02438-7
Received by editor(s): May 5, 1998
Received by editor(s) in revised form: September 15, 1998
Published electronically: April 18, 2000
Additional Notes: This work was partially supported by NSF Grant DMS 91-01424 and NSA grant MDA 904-97-1-0010.
Article copyright: © Copyright 2000 American Mathematical Society

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