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Pré-Publication, Document De Travail Année : 2020

Tits' type alternative for groups acting on toric affine varieties

Résumé

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.
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Dates et versions

hal-02494577 , version 1 (28-02-2020)
hal-02494577 , version 2 (09-03-2020)
hal-02494577 , version 3 (21-09-2020)
hal-02494577 , version 4 (04-11-2020)

Identifiants

Citer

Ivan Arzhantsev, M Zaidenberg. Tits' type alternative for groups acting on toric affine varieties. 2020. ⟨hal-02494577v4⟩

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