Infiniteness of the fundamental groups of a series of \(3\)-manifolds (Q5936682)
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scientific article; zbMATH DE number 1614363
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infiniteness of the fundamental groups of a series of \(3\)-manifolds |
scientific article; zbMATH DE number 1614363 |
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Infiniteness of the fundamental groups of a series of \(3\)-manifolds (English)
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4 July 2001
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The author treats the groups \(G(2n+1)\) with balanced presentation \[ G(2n+1)=\langle a,b\mid b(ab)^n=(ab)^na,\;a(b^2a^2)^{n-1}b^2a=(ba)^{n-1}b,\;n\geq 2\rangle. \] The main result of the paper is as follows: for \(n\geq 2\) all the groups \(G(2n+1)\) are infinite.
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infinite groups
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fundamental groups
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balanced presentations
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