Submission date: 26 September 2022

Abstract:

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 ⟨ δ ⟩ = ⟨ γ ⟩ 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.

Mathematics Subject Classification: 20G15 (20F12, 03C98)

Keywords and phrases:

Full text arXiv 2209.13037: pdf, ps.