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manuscripta mathematica

, Volume 99, Issue 3, pp 329–339 | Cite as

Difference algebraic subgroups of commutative algebraic groups over finite fields

  • Thomas Scanlon
  • José Felipe Voloch

Abstract:

We study the question of which torsion subgroups of commutative algebraic groups over finite fields are contained in modular difference algebraic groups for some choice of a field automorphism. We show that if G is a simple commutative algebraic group over a finite field of characteristic p, ? is a prime different from p, and for some difference closed field (?, σ) the ?-primary torsion of G(?) is contained in a modular group definable in (?, σ), then it is contained in a group of the form {xG(?) :σ(x) =[a](x) } with a∈ℕ\p . We show that no such modular group can be found for many G of interest. In the cases that such equations may be found, we recover an effective version of a theorem of Boxall.

Keywords

Algebraic Group Finite Field Modular Group Effective Version Torsion Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Thomas Scanlon
    • 1
  • José Felipe Voloch
    • 2
  1. 1.Mathematics Department, University of California at Berkeley, Evans Hall, Berkeley, CA 94720, USA. e-mail: scanlon@math.berkeley.eduUS
  2. 2.Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA. e-mail: voloch@math.utexas.eduUS

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