#### Vol. 5, No. 3, 2011

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Toric-friendly groups

### Mikhail Borovoi and Zinovy Reichstein

Vol. 5 (2011), No. 3, 361–378
##### Abstract

Let $G$ be a connected linear algebraic group over a field $k$. We say that $G$ is toric-friendly if for any field extension $K∕k$ and any maximal $K$-torus $T$ in $G$ the group $G\left(K\right)$ acts transitively on $\left(G∕T\right)\left(K\right)$. Our main result is a classification of semisimple (and under certain assumptions on $k$, of connected) toric-friendly groups.

##### Keywords
toric-friendly group, linear algebraic group, semisimple group, maximal torus, rational point, elementary obstruction
##### Mathematical Subject Classification 2000
Primary: 20G10
Secondary: 20G15, 14G05
##### Milestones
Received: 3 April 2010
Revised: 17 October 2010
Accepted: 17 October 2010
Published: 10 September 2011

Proposed: Jean-Louis Colliot-Th\e'l\e`ne
Seconded: Andrei Zelevinsky, Hendrik W. Lenstra
##### Authors
 Mikhail Borovoi Tel Aviv University School of Mathematical Sciences 69978 Tel Aviv Israel http://www.math.tau.ac.il/~borovoi Zinovy Reichstein University of British Columbia Department of Mathematics 1984 Mathematics Road Vancouver, BC V6T 1Z2 Canada http://www.math.ubc.ca/~reichst