Wreath products and subgroups of division rings. (Q2497434)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wreath products and subgroups of division rings. |
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Wreath products and subgroups of division rings. (English)
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4 August 2006
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In this paper the author obtains the following result: Let \(H\) be a finitely generated torsion-free nilpotent group and let \(A\) be a free Abelian group of countable rank. Then the wreath product of \(A\) by \(H\) can be embedded in the skew field of fractions of a suitable chosen finitely generated torsion-free nilpotent group. Comment: To make it clear to the reader in the general ring theory, the conclusion of the above theorem should be: ``Then the wreath product of \(A\) by \(H\) is embedded in the skew field of fractions of the group ring \(\mathbb{Z} G\) where \(G\) is a suitable chosen finitely generated torsion-free nilpotent group'' (unless the author gives a definition of the skew field of fractions of a group).
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wreath products
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group rings
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finitely generated torsion-free nilpotent groups
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skew fields of fractions
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