TY - JOUR

T1 - Uniform independence in linear groups

AU - Breuillard, E.

AU - Gelander, T.

PY - 2008/8

Y1 - 2008/8

N2 - 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.

AB - 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.

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U2 - 10.1007/s00222-007-0101-y

DO - 10.1007/s00222-007-0101-y

M3 - Article

AN - SCOPUS:45849107604

SN - 0020-9910

VL - 173

SP - 225

EP - 263

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 2

ER -