Linear groups with Borel's property

  • Khalil Bou-Rabee

    The City College of New York, USA
  • Michael Larsen

    Indiana University, Bloomington, USA


When does Borel’s theorem on free subgroups of semisimple groups generalize to other groups? We initiate a systematic study of this question and find positive and negative answers for it. In particular, we fully classify fundamental groups of surfaces and von Dyck groups that satisfy Borel’s theorem. Further, as a byproduct of this theory, we make headway on a question of Breuillard, Green, Guralnick, and Tao concerning double word maps.

Cite this article

Khalil Bou-Rabee, Michael Larsen, Linear groups with Borel's property. J. Eur. Math. Soc. 19 (2017), no. 5, pp. 1293–1330

DOI 10.4171/JEMS/693