Uniform independence in linear groups

Details Uniform independence in linear groups Uniform independence in linear groups

2006-11-27

arxiv.org/abs/math/0611829v1

Mathematics

Group Theory

Scientific paper

We show that for any finitely generated group of matrices that is not virtually solvable, 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.

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