Open Access
Fall 2009 The maximal pure spectrum of an Abelian group
R. Göbel, B. Goldsmith
Illinois J. Math. 53(3): 817-832 (Fall 2009). DOI: 10.1215/ijm/1286212917

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.

Citation

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R. Göbel. B. Goldsmith. "The maximal pure spectrum of an Abelian group." Illinois J. Math. 53 (3) 817 - 832, Fall 2009. https://doi.org/10.1215/ijm/1286212917

Information

Published: Fall 2009
First available in Project Euclid: 4 October 2010

zbMATH: 1210.20052
MathSciNet: MR2727356
Digital Object Identifier: 10.1215/ijm/1286212917

Subjects:
Primary: 20K10 , 20K20 , 20K27

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

Vol.53 • No. 3 • Fall 2009
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