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Gröbnerian Dickson polynomials


Authors: Müfit Sezer and Özgün Ünlü
Journal: Proc. Amer. Math. Soc. 137 (2009), 1169-1173
MSC (2000): Primary 13A50
DOI: https://doi.org/10.1090/S0002-9939-08-09758-X
Published electronically: November 17, 2008
MathSciNet review: 2465636
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Abstract: Let $ F$ be a finite field and $ k$ be a positive integer. We compute the reduced Gröbner basis for the Hilbert ideal of $ GL_k(F)$ in terms of Dickson invariants of its subgroups.


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

  • 1. H. E. A. Campbell, I. P. Hughes, R. J. Shank, and D. L. Wehlau, Bases for rings of coinvariants, Transform. Groups 1 (1996), no. 4, 307-336. MR 1424447 (98a:13011)
  • 2. Leonard Eugene Dickson, A fundamental system of invariants of the general modular linear group with a solution of the form problem, Trans. Amer. Math. Soc. 12 (1911), no. 1, 75-98. MR 1500882
  • 3. Robert Steinberg, On Dickson's theorem on invariants, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), no. 3, 699-707. MR 927606 (89c:11177)
  • 4. Bernd Sturmfels, Gröbner bases and convex polytopes, University Lecture Series, vol. 8, American Mathematical Society, Providence, RI, 1996. MR 1363949 (97b:13034)
  • 5. Clarence Wilkerson, A primer on the Dickson invariants, Proceedings of the Northwestern Homotopy Theory Conference (Evanston, Ill., 1982), Contemp. Math., vol. 19, Amer. Math. Soc., Providence, RI, 1983, pp. 421-434. MR 711066 (85c:55017)

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Additional Information

Müfit Sezer
Affiliation: Department of Mathematics, Bilkent University, Ankara 06800, Turkey

Özgün Ünlü
Affiliation: Department of Mathematics, Bilkent University, Ankara 06800, Turkey

DOI: https://doi.org/10.1090/S0002-9939-08-09758-X
Keywords: Dickson polynomials, Gr\"{o}bner basis, Hilbert ideal
Received by editor(s): February 25, 2008
Published electronically: November 17, 2008
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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