Mathematics – Group Theory
Scientific paper
2010-10-20
Mathematics
Group Theory
27 pages, no figures, submitted, Israel J. Math. It turns out that there is one specific family of algebraic group - namely Sp
Scientific paper
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.
Breuillard Emmanuel
Green Ben
Guralnick Robert
Tao Terence
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