Uniform independence in linear groups. (Q938282)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform independence in linear groups. |
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Uniform independence in linear groups. (English)
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19 August 2008
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Tits's alternative says that if \(\Gamma\) is a finitely generated group of matrices over a field which does not contain a solvable subgroup of finite index then \(\Gamma\) contains two elements which generate a non-Abelian free subgroup. The authors show that there are such two elements (depending on the finite generating set) with bounded length with respect to any finite generating set.
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Tits alternative
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finitely generated groups of matrices
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solvable subgroups of finite index
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non-Abelian free subgroups
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finite generating sets
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