Tits type alternative for groups acting on toric affine varieties
Abstract
Given a toric affine algebraic variety $X$ and a collection of oneparameter unipotent subgroups $U_1,\ldots,U_s$ of $\mathop{\rm Aut}(X)$ which are normalized by the torus acting on $X$, we show that the group $G$ generated by $U_1,\ldots,U_s$ verifies the following alternative of Tits' type: either $G$ is a unipotent algebraic group, or it contains a nonabelian free subgroup. We deduce that if $G$ is $2$transitive on a $G$orbit in $X$, then $G$ contains a nonabelian free subgroup, and so, is of exponential growth.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2003.00037
 Bibcode:
 2020arXiv200300037A
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Group Theory;
 14R20 (primary);
 20B22 (secondary)
 EPrint:
 24 pages. The main result strengthened, the proof of Proposition 4.8 written in more detail