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Slenderness, Completions, and Duality for Primary Abelian Groups

✍ Scribed by Patrick Keef

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 191 KB
Volume: 187
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.6797

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✦ Synopsis

If A is a fixed abelian group with endomorphism ring E, then for any group G, Ž . Ž . let G* s Hom G, A and for any E-module M, let M* s Hom M, A . The E evaluation map : G ª G** is defined in the usual way and G is A-reflexive if G is an isomorphism. This is strongly related to the question of whether A is G slender as an E-module, and we discuss the p-groups for which this holds. In some important cases, G** can be viewed as the completion of G in a linear topology. It is known that if A s [ Z n, and G is a p-group of non-measurable cardinality, p n then G** can be identified with the completion of G in the [-topology, and we c provide a generalization of this result. We also show that for any group N of Ž . non-measurable cardinality there is a group G such that G**r G ( N.

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