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arXiv · 1312.7294

Linear groups with Borel's property

Khalid Bou-Rabee·Michael Larsen
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Abstract

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.

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Khalid Bou-Rabee, Michael Larsen. 2013-12-27. Linear groups with Borel's property. https://arxiv.org/abs/1312.7294

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