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 -