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arXiv · 1510.04144

Zariski Closures and Subgroup Separability

Larsen Louder·D. B. McReynolds·Priyam Patel
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Abstract

The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a free or surface group.

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Larsen Louder, D. B. McReynolds, Priyam Patel. 2015-10-14. Zariski Closures and Subgroup Separability. https://arxiv.org/abs/1510.04144

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