Illinois Journal of Mathematics

The maximal pure spectrum of an Abelian group

R. Göbel and B. Goldsmith

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This paper introduces the notion of the maximal pure spectrum of an Abelian group—this is the set of isomorphism classes of maximal proper pure subgroups—and focuses on the situation in which this spectrum is small. The converse situation is also examined i.e., given a collection of isomorphism classes of groups, can one find an Abelian group having precisely this collection as its maximal pure spectrum. Finally, it is shown that in some familiar situations, the answers to these questions may be undecidable.

Article information

Illinois J. Math., Volume 53, Number 3 (2009), 817-832.

First available in Project Euclid: 4 October 2010

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Zentralblatt MATH identifier

Primary: 20K27: Subgroups 20K20: Torsion-free groups, infinite rank 20K10: Torsion groups, primary groups and generalized primary groups


Göbel, R.; Goldsmith, B. The maximal pure spectrum of an Abelian group. Illinois J. Math. 53 (2009), no. 3, 817--832. doi:10.1215/ijm/1286212917.

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