Displaying similar documents to “Various local global principles for abelian groups.”

P-localization of some classes of groups.

Augusto Reynol Filho (1993)

Publicacions Matemàtiques

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The aim for the present paper is to study the theory of P-localization of a group in a category C such that it contains the category of the nilpotent groups as a full sub-category. In the second section we present a number of results on P-localization of a group G, which is the semi-direct product of an abelian group A with a group X, in the category G of all groups. It turns out that the P-localized (G) is completely described by the P-localized X of X, A and the action w of X on A....

On finite abelian groups realizable as Mislin genera.

Peter Hilton, Dirk Scevenels (1997)

Publicacions Matemàtiques

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We study the realizability of finite abelian groups as Mislin genera of finitely generated nilpotent groups with finite commutator subgroup. In particular, we give criteria to decide whether a finite abelian group is realizable as the Mislin genus of a direct product of nilpotent groups of a certain specified type. In the case of a positive answer, we also give an effective way of realizing that abelian group as a genus. Further, we obtain some non-realizability results.

On induced morphism of Mislin genera.

Peter Hilton (1994)

Publicacions Matemàtiques

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Let N be a nilpotent group with torsion subgroup TN, and let α: TN → T' be a surjective homomorphism such that kerα is normal in N. Then α determines a nilpotent group Ñ such that TÑ = T' and a function α from the Mislin genus of N to that of Ñ in N (and hence Ñ) is finitely generated. The association α → α satisfies the usual functiorial conditions. Moreover [N,N] is finite if and only if [Ñ,Ñ] is finite and α is then a homomorphism of abelian groups. If Ñ belongs to the special class...

On localizations of torsion abelian groups

José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann (2004)

Fundamenta Mathematicae

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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...