On the Kneser–Tits problem for triality forms

Abstract

The purpose of this paper is to provide a concrete description of the “Whitehead group” W(k,G) := G(k)/G(k)+ for the simply connected triality forms G of k-rank 1, and to use this description to prove that if k is a global field, then the Kneser–Tits problem for these forms has an affirmative solution.