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.
- Shreeram S. Abhyankar, Nice equations for nice groups, Israel J. Math. 88 (1994), no. 1-3, 1–23. MR 1303488, DOI https://doi.org/10.1007/BF02937504
- Shreeram S. Abhyankar, Projective polynomials, Proc. Amer. Math. Soc. 125 (1997), no. 6, 1643–1650. MR 1403111, DOI https://doi.org/10.1090/S0002-9939-97-03939-7
- S. S. Abhyankar, Galois theory of semilinear transformations, London Math. Soc. Lecture Note Ser., 256, Cambridge Univ. Press, Cambridge, 1999.
- E. Artin, Geometric Algebra, Interscience, 1957.
- R. W. Carter, Simple Groups of Lie Type, Wiley, 1977.
- Peter Dembowski, Finite geometries, Classics in Mathematics, Springer-Verlag, Berlin, 1997. Reprint of the 1968 original. MR 1434062
- J. Dieudonné, On the Automorphisms of the Classical Groups, Memoirs of the American Mathematical Society No. 2, 1951.
- J. Dieudonné, La Géométrie des Groupes Classiques, Springer-Verlag, 1955.
- L. K. Hua, On the automorphisms of the symplectic group over any field, Annals of Mathematics 49 (1948), 739-759.
- Jean Dieudonné, On the automorphisms of the classical groups, Memoirs of the American Mathematical Society, No. 2, American Mathematical Society, Providence, R.I., 1980. With a supplement by Loo Keng Hua [Luo Geng Hua]; Reprint of the 1951 original. MR 606555
- O. Schreier and B. L. van der Waerden, Die Automorphismen der projectiven Gruppen, Abhand. Math. Seminar Univ. Hamburg 6 (1928), 303-322.
- Robert Steinberg, Automorphisms of finite linear groups, Canadian J. Math. 12 (1960), 606–615. MR 121427, DOI https://doi.org/10.4153/CJM-1960-054-6
- Michio Suzuki, Gun ron. Vol. 1, Gendai Sūgaku [Modern Mathematics], vol. 18, Iwanami Shoten, Tokyo, 1977 (Japanese). MR 514842
- 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
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