Constructing free groups in a normal subgroup of the multiplicative group of division rings. (Q500218)
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scientific article; zbMATH DE number 6488159
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Constructing free groups in a normal subgroup of the multiplicative group of division rings. |
scientific article; zbMATH DE number 6488159 |
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Constructing free groups in a normal subgroup of the multiplicative group of division rings. (English)
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1 October 2015
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Let \(D\) be a division ring and \(N\) be a normal subgroup of the multiplicative group \(D^*\) of \(D\). From previous results of Lichtman it follows that if \(N\) contains a nonabelian torsion-free polycyclic-by-finite subgroup \(G\) then \(N\) contains a free noncyclic subgroup. In the article under review, the author provides some method to construct this free subgroup of \(N\) in terms of elements of \(G\).
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multiplicative groups of division rings
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normal subgroups
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free subgroups
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polycyclic-by-finite subgroups
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