## Illinois Journal of Mathematics

### The maximal pure spectrum of an Abelian group

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 4 October 2010

https://projecteuclid.org/euclid.ijm/1286212917

Digital Object Identifier
doi:10.1215/ijm/1286212917

Mathematical Reviews number (MathSciNet)
MR2727356

Zentralblatt MATH identifier
1210.20052

#### Citation

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. https://projecteuclid.org/euclid.ijm/1286212917

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