• Corpus ID: 252545162

Powers of commutators in linear algebraic groups

  title={Powers of commutators in linear algebraic groups},
  author={Benjamin Martin},
  • B. Martin
  • Published 26 September 2022
  • Mathematics
. Let G be a linear algebraic group over k , where k is an algebraically closed field, a pseudo-finite field or the valuation ring of a nonarchimedean local field. Let G = G ( k ). We prove that if γ, δ ∈ G such that γ is a commutator and h δ i = h γ i then δ is a commutator. This generalises a result of Honda for finite groups. Our proof uses the Lefschetz Principle from first-order model theory. 



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