# Tits alternative and highly transitive actions on toric varieties

@article{Arzhantsev2020TitsAA, title={Tits alternative and highly transitive actions on toric varieties}, author={Ivan Arzhantsev and M. Zaidenberg}, journal={arXiv: Algebraic Geometry}, year={2020} }

Given a toric affine algebraic variety $X$ and a collection of one-parameter unipotent subgroups $U_1,\ldots,U_s$ of ${\rm Aut}(X)$ which are normalized by the torus acting on $X$, we show that the group $G$ generated by $U_1,\ldots,U_s$ verifies the Tits alternative, and, moreover, either is a unipotent algebraic group, or contains a nonabelian free subgroup. We deduce that if $G$ is $m$-transitive for any positive integer $m$, then $G$ contains a nonabelian free subgroup, and so, is of…

## One Citation

Some finiteness results on triangular automorphisms

- Mathematics
- 2020

In this note we prove that every finite collection of connected algebraic subgroups of the group of triangular automorphisms of the affine space generates a connected solvable algebraic subgroup.

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