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.
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}
}