# Powers of commutators in linear algebraic groups

@inproceedings{Martin2022PowersOC, title={Powers of commutators in linear algebraic groups}, author={Benjamin Martin}, year={2022} }

. 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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