Louder, L;
McReynolds, DB;
Patel, P;
(2017)
Zariski closures and subgroup separability.
Selecta Mathematica
, 23
(3)
pp. 2019-2027.
10.1007/s00029-016-0300-8.
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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.
| Type: | Article |
|---|---|
| Title: | Zariski closures and subgroup separability |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00029-016-0300-8 |
| Publisher version: | http://doi.org/ 10.1007/s00029-016-0300-8 |
| Language: | English |
| Additional information: | © 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | 20E05; 20E26 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1527619 |
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