zbMATH — the first resource for mathematics

The Whitehead groups of algebraic groups and applications to some problems of algebraic group theory. (English) Zbl 0832.20072
Bokut’, L. A. (ed.) et al., Third Siberian school on algebra and analysis. Proceedings of the third Siberian school, Irkutsk State University, Irkutsk, Russia, August 30-September 4, 1989. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 163, 127-134 (1995).
Let $$G$$ be an algebraic group defined over an infinite field $$k = 2k$$. Assuming that $$G$$ is absolutely simple and $$k$$-isotropic, let $$G(k)^+$$ be a subgroup of $$G(k)$$ generated by root elements. The group $$G(l)/G(k)^+$$ is investigated and its connections with $$k$$- rationality, weak approximation, and $$R$$-equivalence for $$G$$ are discussed.
For the entire collection see [Zbl 0816.00016].
MSC:
 20G15 Linear algebraic groups over arbitrary fields 19B14 Stability for linear groups