English

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.

Keywords

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

R2 v1 2026-06-22T02:35:47.913Z