English

Uniform independence in linear groups

Group Theory 2007-05-23 v1

Abstract

We show that for any finitely generated group of matrices that is not virtually solvable, there is an integer m such that, given an arbitrary finite generating set for the group, one may find two elements a and b that are both products of at most m generators, such that a and b are free generators of a free subgroup. This uniformity result improves the original statement of the Tits alternative.

Keywords

Cite

@article{arxiv.math/0611829,
  title  = {Uniform independence in linear groups},
  author = {E. Breuillard and T. Gelander},
  journal= {arXiv preprint arXiv:math/0611829},
  year   = {2007}
}