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Algebraic groups over finite fields, a quick proof of Lang's theorem


Author: Peter Müller
Journal: Proc. Amer. Math. Soc. 131 (2003), 369-370
MSC (2000): Primary 20G40
DOI: https://doi.org/10.1090/S0002-9939-02-06591-7
Published electronically: May 17, 2002
MathSciNet review: 1933326
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Abstract: We give an easy proof of Lang's theorem about the surjectivity of the Lang map $g\mapsto g^{-1}F(g)$ on a linear algebraic group defined over a finite field, where $F$ is a Frobenius endomorphism.


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

  • 1. Armand Borel, Linear algebraic groups, second ed., Springer-Verlag, New York, 1991. MR 92d:20001
  • 2. François Digne and Jean Michel, Representations of finite groups of Lie type, Cambridge University Press, Cambridge, 1991. MR 92g:20063
  • 3. James E. Humphreys, Linear algebraic groups, Springer-Verlag, New York, 1975, Graduate Texts in Mathematics, No. 21. MR 53:633
  • 4. Serge Lang, Algebraic groups over finite fields, Amer. J. Math. 78 (1956), 555-563. MR 19:174a
  • 5. T. A. Springer, Linear algebraic groups, Birkhäuser Boston, Mass., 1981. MR 84i:20002
  • 6. Robert Steinberg, On theorems of Lie-Kolchin, Borel, and Lang, Contributions to algebra (collection of papers dedicated to Ellis Kolchin), Academic Press, New York, 1977, pp. 349-354. MR 57:6216

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Additional Information

Peter Müller
Affiliation: IWR, Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany
Email: Peter.Mueller@iwr.uni-heidelberg.de

DOI: https://doi.org/10.1090/S0002-9939-02-06591-7
Received by editor(s): August 23, 2001
Received by editor(s) in revised form: September 26, 2001
Published electronically: May 17, 2002
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society

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