A Strong Tits Alternative
نویسنده
چکیده
We show that for every integer d ∈ N, there is N(d) ∈ N such that if K is any field and F is a finite subset of GLd(K), which generates a non amenable subgroup, then F 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 subgroups of GLd(Fq) as well as other diophantine properties of non-discrete subgroups of Lie groups.
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تاریخ انتشار 2008