Linear groups with Borel's property
Khalil Bou-RabeeThe City College of New York, USA
Michael LarsenIndiana 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. 1293–1330DOI 10.4171/JEMS/693