\(P\)-nilpotent completion is not idempotent (Q1385192)
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scientific article; zbMATH DE number 1146197
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(P\)-nilpotent completion is not idempotent |
scientific article; zbMATH DE number 1146197 |
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\(P\)-nilpotent completion is not idempotent (English)
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20 October 1998
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Let \(P\) be an arbitrary set of primes. It is proved that the \(P\)-nilpotent completion of an infinitely generated free group \(F\) does not induce an isomorphism on the first homology group with \(\mathbb{Z}_p\) coefficients. As a consequence, the \(P\)-nilpotent completion is not idempotent and any infinite wedge of circles is \(R\)-bad, where \(R\) is any subring of the rationals.
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\(P\)-nilpotent completions
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infinitely generated free groups
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first homology groups
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wedges of circles
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