On exponential growth rates for free groups (Q1281296)
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scientific article; zbMATH DE number 1267260
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On exponential growth rates for free groups |
scientific article; zbMATH DE number 1267260 |
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On exponential growth rates for free groups (English)
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2 November 1999
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It is well known that, with respect to any basis of a free group \(F_n\) of rank \(n\), the exponential growth rate is \(2n-1\). It is shown in the paper that the exponential growth rate of a group \(G\) with respect to an \(n\)-element generating set \(X\) is \(2n-1\) if and only if \(G\) is free on \(X\).
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free groups
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word lengths
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exponential growth rates
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generating sets
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groups of exponential growth
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