Tits alternative for maximal subgroups of \(\text{GL}_n(D)\). (Q1421816)
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scientific article; zbMATH DE number 2037101
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tits alternative for maximal subgroups of \(\text{GL}_n(D)\). |
scientific article; zbMATH DE number 2037101 |
Statements
Tits alternative for maximal subgroups of \(\text{GL}_n(D)\). (English)
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3 February 2004
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Let \(D\) be a noncommutative, finite-dimensional, division algebra. Suppose \(M\) is a maximal subgroup of \(\text{GL}(n,D)\) that does not contain a noncyclic free subgroup. The author describes the structure of this \(M\). In particular \(M\) is Abelian-by-finite if \(\text{char\,}D=0\) and is Abelian-by-locally-finite otherwise.
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free subgroups
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division rings
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maximal subgroups
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general linear groups
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