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Nice elongations of primary abelian groups
Danchev, Peter V. (Plovdiv University “Paisii Hilendarski” (Bulgària). Department of Mathematics)
Keef, Patrick W. (Whitman College (Regne Unit). Department of Mathematics)

Data: 2010
Resum: Suppose N is a nice subgroup of the primary abelian group G and A = G/N. The paper discusses various contexts in which G satisfying some property implies that A also satisfies the property, or visa versa, especially when N is countable. For example, if n is a positive integer, G has length not exceeding ω1 and N is countable, then G is n-summable iff A is n-summable. When A is separable and N is countable, we discuss the condition that any such G decomposes into the direct sum of a countable and a separable group, and we show that it is undecidable in ZFC whether this condition implies that A must be a direct sum of cyclics. We also relate these considerations to the study of nice bases for primary abelian groups.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Nice subgroups ; Elongations ; Abelian groups ; w1 -homomorphisms
Publicat a: Publicacions Matemàtiques, Vol. 54, Núm. 2 (2010) , p. 317-339, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_54210_02

23 p, 237.6 KB

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