Open Access
2010 Nice Elongations of Primary Abelian Groups
Peter V. Danchev, Patrick W. Keef
Publ. Mat. 54(2): 317-339 (2010).


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 $\omega_1$ and $N$ is countable, then $G$ is $n$-summable if $A$ 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.


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Peter V. Danchev. Patrick W. Keef. "Nice Elongations of Primary Abelian Groups." Publ. Mat. 54 (2) 317 - 339, 2010.


Published: 2010
First available in Project Euclid: 28 June 2010

zbMATH: 1214.20055
MathSciNet: MR2675926

Primary: 20K10

Keywords: $\omega_1$-homomorphisms , Abelian groups , elongations , Nice subgroups

Rights: Copyright © 2010 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.54 • No. 2 • 2010
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