The \(\Sigma^2\)-conjecture for metabelian groups and some new conjectures: the split extension case (Q1969359)
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scientific article; zbMATH DE number 1416171
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(\Sigma^2\)-conjecture for metabelian groups and some new conjectures: the split extension case |
scientific article; zbMATH DE number 1416171 |
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The \(\Sigma^2\)-conjecture for metabelian groups and some new conjectures: the split extension case (English)
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6 May 2001
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The \(\Sigma^2\)-conjecture for metabelian groups is discussed, and it is proved to be true in the case of split extensions. Note that the \(\Sigma^m\)-conjecture is still an open problem in the general case, and that the proofs given here are inspired by the geometric methods introduced by \textit{R. Bieri} and \textit{R. Strebel} [Proc. Lond. Math. Soc., III. Ser. 41, 439-464 (1980; Zbl 0448.20029)] in order to prove the \(FP_2\)-conjecture for finitely generated metabelian groups.
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metabelian groups
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\(\Sigma^2\)-conjecture
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