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arXiv · 1010.4259

Strongly dense free subgroups of semisimple algebraic groups

Emmanuel Breuillard·Ben Green·Robert Guralnick·Terence Tao
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Abstract

We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense. As a consequence, we get new generating results for finite simple groups of Lie type and a strengthening of a theorem of Borel related to the Hausdorff-Banach-Tarski paradox. In a sequel to this paper, we use this result to also establish uniform expansion properties for random Cayley graphs over finite simple groups of Lie type.

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Emmanuel Breuillard, Ben Green, Robert Guralnick, Terence Tao. 2010-10-20. Strongly dense free subgroups of semisimple algebraic groups. https://arxiv.org/abs/1010.4259

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