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On the rationalization of the circle


Author: Carles Casacuberta
Journal: Proc. Amer. Math. Soc. 118 (1993), 995-1000
MSC: Primary 55P60; Secondary 20J05
DOI: https://doi.org/10.1090/S0002-9939-1993-1176479-3
MathSciNet review: 1176479
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Abstract: We give an example showing that, for a nilpotent group $ G$ and a set of primes $ P$, the $ P$-localization homomorphism $ l:G \to {G_P}$ need not induce an isomorphism in cohomology with arbitrary (twisted) $ {{\mathbf{Z}}_P}$-module coefficients. From this fact we infer that, in the pointed homotopy category of connected CW-complexes, the inclusion of the subcategory of spaces whose higher homotopy groups are $ {{\mathbf{Z}}_P}$-modules and whose fundamental group is uniquely $ {P'}$-radicable does not admit a left adjoint.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1176479-3
Article copyright: © Copyright 1993 American Mathematical Society

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