Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

CNPq-Brazil[302.756/82-5]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fapesp[Tematico 00/07.291-0]

NSERC, Canada

NSERC, Canada