Linear groups with Borel's property

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.


Date Submitted:
Nov 21 2018
ISSN:
1435-9863
Citation:
Journal of the European Mathematical Society
5
Note:
A freely accessible, full text version is available using the link(s) in External Resources.
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 Record created 2018-11-21, last modified 2019-04-03


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