Kneser–Tits conjecture

In mathematics, the Kneser–Tits problem, introduced by Tits (1964) based on a suggestion by Martin Kneser, asks whether the Whitehead group W(G,K) of a semisimple simply connected isotropic algebraic group G over a field K is trivial.

["Généralisant le problème de Tannaka-Artin, M.Kneser a posé la question suivante que j’ai imprudemment transformé en conjecture."

The Whitehead group is the quotient of the rational points of G by the normal subgroup generated by K-subgroups isomorphic to the additive group.

A special case of the Kneser–Tits problem asks for which fields the Whitehead group of a semisimple almost simple simply connected isotropic algebraic group is always trivial.

For global fields the combined work of several authors shows that this Whitehead group is always trivial (Gille 2009).