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Noetherian loop spaces

Natàlia Castellana;  Juan Crespo;  Jérôme Scherer — 2011

Journal of the European Mathematical Society

The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p -compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as ℂ P ∞ and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space B X of such an object and prove it is as small as expected, that is, comparable to that of B ℂ P ∞ . We also show that B X differs basically from the classifying space of a p -compact group...

On localizations of torsion abelian groups

José L. Rodríguez;  Jérôme Scherer;  Lutz Strüngmann — 2004

Fundamenta Mathematicae

As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by | T | ℵ ₀ whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of the localization of the primary components of T in many cases. Furthermore, we completely characterize the relationship...

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