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


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.


Algebraic Group Finite Field Modular Group Effective Version Torsion Subgroup 
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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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