English

Strongly dense free subgroups of semisimple algebraic groups II

Group Theory 2022-12-19 v1

Abstract

It was shown in Part I that there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski-dense. Here we show that the same is true for as long as the transcendence degree of the field is at least 11 in characteristic zero and at least 22 in positive characteristic. We also consider related questions for surface groups.

Keywords

Cite

@article{arxiv.2212.08114,
  title  = {Strongly dense free subgroups of semisimple algebraic groups II},
  author = {Emmanuel Breuillard and Robert Guralnick and Michael Larsen},
  journal= {arXiv preprint arXiv:2212.08114},
  year   = {2022}
}