• Corpus ID: 9711439

# A Strong Tits Alternative

@article{Breuillard2008AST,
title={A Strong Tits Alternative},
author={Emmanuel Breuillard},
journal={arXiv: Group Theory},
year={2008}
}
• E. Breuillard
• Published 9 April 2008
• Mathematics
• arXiv: Group Theory
We show that for every integer $d$, there is a constant $N(d)$ such that if $K$ is any field and $F$ is a finite subset of $GL_d(K)$, which generates a non amenable subgroup, then $F^{N(d)}$ contains two elements, which freely generate a non abelian free subgroup. This improves the original statement of the Tits alternative. It also implies a growth gap and a co-growth gap for non-amenable linear groups, and has consequences about the girth and uniform expansion of small sets in finite…
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