Kneser–Tits conjecture for simply connected isotropic almost simple groups

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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.

References

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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