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1993-07

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/96487

On the rationalization of the circle

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http://dx.doi.org/10.1090/S0002-9939-1993-1176479-3

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.

Subject

Teoria de l'homotopia, Teoria de grups

Subject (English)

Homotopy theory, Group theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CASACUBERTA, Carles. On the rationalization of the circle. Proceedings of the American Mathematical Society. 1993. Vol. 118, num. 3, pags. 995-1000. ISSN 0002-9939. [consulted: 14 of August of 2026]. Available at: https://hdl.handle.net/2445/96487

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