\(P\)-nilpotent completion is not idempotent
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.
scientific article; zbMATH DE number 1146197