Casacuberta, Carles2016-03-152016-03-151993-070002-9939https://hdl.handle.net/2445/96487We 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.6 p.application/pdfeng(c) American Mathematical Society (AMS), 1993Teoria de l'homotopiaTeoria de grupsHomotopy theoryGroup theoryinfo:eu-repo/semantics/article5837552016-03-15info:eu-repo/semantics/openAccess