Tits type alternative for groups acting on toric affine varieties
| Autor: | Arzhantsev, I., Zaidenberg, M. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | International Mathematics Research Notices (IMRN) 2022 (2022), no. 11, 8162-8195 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1093/imrn/rnaa342 |
| Popis: | Given a toric affine algebraic variety $X$ and a collection of one-parameter 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 non-abelian free subgroup. We deduce that if $G$ is $2$-transitive on a $G$-orbit in $X$, then $G$ contains a non-abelian free subgroup, and so, is of exponential growth. Comment: 24 pages. The main result strengthened, the proof of Proposition 4.8 written in more detail; some references added; the referee remarks taken into account; the title changed |
| Databáze: | arXiv |
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