A bound for groups of linear growth (Q1070340)
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scientific article; zbMATH DE number 3935306
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bound for groups of linear growth |
scientific article; zbMATH DE number 3935306 |
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A bound for groups of linear growth (English)
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1987
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Let G be a finitely generated group and let f(n) be the number of elements which can be represented by words of length \(\leq n\) in the generators or their inverses. Suppose G is infinite, \(k>0\), and f(k)-f(k- 1)\(\leq k\). Set \(c=f(k)-f(k-1)\). It is shown that G has a subgroup isomorphic to \({\mathbb{Z}}\) of index \(\leq c\) and that this bound is sharp.
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finitely generated group
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cyclic subgroup of finite index
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0.97222817
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0.91742563
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0.91656923
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0.9133338
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0.9106578
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