• 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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37 Citations
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37 Citations

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A Height Gap Theorem For Finite Subsets Of GL_d(\bar{Q}) and Non Amenable Subgroups
We show a global adelic analog of the classical Margulis Lemma from hyperbolic geometry. We introduce a conjugation invariant normalized height $\hat{h}(F)$ of a finite set of matrices $F$ in…
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