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3.42 (1969)

Solved

(Kneser–Tits conjecture). Let $G$ be a simply connected $k$-defined simple algebraic group, and $E_k(G)$ the subgroup generated by unipotent $k$-elements. If $E_k(G) \neq 1$, then $G_k = E_k(G)$. The proof is known for $k$-decomposable groups (C. Chevalley) and for local fields (V. P. Platonov).

Contributor: V. P. Platonov

Progress

The conjecture was refuted (V. P. Platonov, Math. USSR–Izv., 10, no. 2 (1976), 211–243).

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