Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Pure mathematics

Publication Details

Illinois Journal of Mathematics, 53 (2009) 817-832 Available from the Publisher here http://ijm.math.illinois.edu/

Abstract

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.

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Mathematics Commons

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