ON A PROPERTY OF SPECIAL GROUPS

ZINOVY REICHSTEIN BORIS YOUSSIN

Abstract. Let G be an algebraic group defined over an algebraically closed field k of characteristic zero. We give a simple proof of the following result: if H^{1}(K_{0}, G) = {1} for some finitely generated field extension K_{0}/k of transcendence degree ≥ 3 then H^{1}(K, G) = {1} for every field extension K/k.