Linear groups with Borel's property
Group Theory
2013-12-30 v1 Representation Theory
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.
Cite
@article{arxiv.1312.7294,
title = {Linear groups with Borel's property},
author = {Khalid Bou-Rabee and Michael Larsen},
journal= {arXiv preprint arXiv:1312.7294},
year = {2013}
}
Comments
38 pages