Linear groups with Borel's property

2013/12/27 by Khalid Bou-Rabee, Michael Larsen, Bou-Rabee, Khalid +1
Mathematics · #20E26 #20F70 #20G05 #20G20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20E26 #msc:20F70 #msc:20G05 #msc:20G20

paper · pdf · doi:10.48550/arxiv.1312.7294

38 pages

arxiv created 2013/12/27 · arxiv updated 2013/12/30

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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