Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the rationalization of the circle

Author: Carles Casacuberta
Journal: Proc. Amer. Math. Soc. 118 (1993), 995-1000
MSC: Primary 55P60; Secondary 20J05
MathSciNet review: 1176479
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55P60, 20J05

Retrieve articles in all journals with MSC: 55P60, 20J05

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society