Primitive elements of the free groups of the varieties \({\mathfrak AN}_n\) (Q1274067)
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scientific article; zbMATH DE number 1238030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Primitive elements of the free groups of the varieties \({\mathfrak AN}_n\) |
scientific article; zbMATH DE number 1238030 |
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Primitive elements of the free groups of the varieties \({\mathfrak AN}_n\) (English)
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12 July 1999
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It is proved that, in contrast to the case of a free metabelian group [see \textit{M. J. Evans}, Can. Math. Bull. 37, No. 4, 468-472 (1994; Zbl 0822.20032)], for a free group of the variety \({\mathfrak AN}_2\), there exists an element \(h\) whose normal closure contains a primitive element \(x\), but the elements \(h\) and \(x^{\pm 1}\) are not conjugate.
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varieties of groups
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relatively free groups
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primitive elements
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normal closures
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Abelian-by-nilpotent groups
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free metabelian groups
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