Uniform independence in linear groups

E. Breuillard*, T. Gelander

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We show that for any non-virtually solvable finitely generated group of matrices over any field, there is an integer m such that, given an arbitrary finite generating set for the group, one may find two elements a and b that are both products of at most m generators, such that a and b are free generators of a free subgroup. This uniformity result improves the original statement of the Tits alternative.

Original languageEnglish (US)
Pages (from-to)225-263
Number of pages39
JournalInventiones Mathematicae
Issue number2
StatePublished - Aug 2008

ASJC Scopus subject areas

  • Mathematics(all)


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