Kneser–Tits conjecture for simply connected isotropic almost simple groups

Let kk be the base field, and let GG be a simply connected, almost kk-simple, kk-isotropic algebraic group over kk. Let G(k)+G(k)^+ denote the abstract subgroup of G(k)G(k) generated by its unipotent elements. Kneser–Tits conjecture.

G(k)+=G(k).G(k)^+=G(k).

This is the Kneser–Tits generation problem for isotropic algebraic groups: it asks whether the rational points are generated by unipotent elements. The source gives no resolution status for the stated form.

Sources & referencesView supporting material

Primary source

Ningyuan Yao and Zhentao Zhang, “Newelski's Conjecture for o-Minimal and p-Adic Groups”, arXiv:2602.01810 (2026).

Additional references

2 papers in this index state this conjecture (2026). The statement above is taken from the most recent of them; the others are arXiv:2601.20565.

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