Zariski closures and subgroup separability

• Larsen Louder ^[1] ; D. B. McReynolds ^[2] ; Priyam Patel ^[3]
  1. [1] University College London

     University College London

     Reino Unido

     
  2. [2] Purdue University

     Purdue University

     Township of Wabash, Estados Unidos

     
  3. [3] University of California

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 2019-2027
• Idioma: inglés
• DOI: 10.1007/s00029-016-0300-8
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• Resumen

  • 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.