Heights on \(\mathrm{SL}_2\) and free subgroups. (Q2908720)
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scientific article; zbMATH DE number 6077155
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Heights on \(\mathrm{SL}_2\) and free subgroups. |
scientific article; zbMATH DE number 6077155 |
Statements
5 September 2012
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Tits alternative
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finitely generated subgroups
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matrix groups over fields
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subgroups of finite index
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Heights on \(\mathrm{SL}_2\) and free subgroups. (English)
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The classical Tits alternative asserts that a finitely generated subgroup of the matrix group \(\mathrm{GL}_d(K)\) over a field \(K\) either contains a nonabelian free group or has a solvable subgroup of finite index. The author recently obtained [Ann. Math. (2) 174, No. 2, 1057-1110 (2011; Zbl 1243.11071) and A strong Tits alternative. \url{arXiv:0804.1395}] a uniform version of this alternative. The present paper gives an exposition of the result in the special case \(d=2\).NEWLINENEWLINEFor the entire collection see [Zbl 1225.00042].
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