Geodesic
Linear groups with Borel's property
Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1293-1330

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DOI

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.
DOI : 10.4171/jems/693
Classification : 20-XX
Keywords: Free groups, linear groups, Borel's property 
Khalil Bou-Rabee; Michael Larsen. Linear groups with Borel's property. Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1293-1330. doi: 10.4171/jems/693
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     author = {Khalil Bou-Rabee and Michael Larsen},
     title = {Linear groups with {Borel's} property},
     journal = {Journal of the European Mathematical Society},
     pages = {1293--1330},
     year = {2017},
     volume = {19},
     number = {5},
     doi = {10.4171/jems/693},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/693/}
}
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