On endomorphism rings of -groups that are not -groups

Author:
Lutz Strüngmann

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3657-3668

MSC (2000):
Primary 20K15, 20K20, 20K35, 20K40; Secondary 18E99, 20J05

Published electronically:
June 15, 2009

MathSciNet review:
2529872

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Abstract | References | Similar Articles | Additional Information

Abstract: Finite rank Butler groups are pure subgroups of completely decomposable groups of finite rank and were defined by M.C.R. Butler. Extending this concept to infinite rank groups, Bican and Salce gave various possible descriptions: A -group is a union of an ascending chain of pure subgroups such that for every we have for some finite rank Butler group . A -group is a torsion-free group satisfying for all torsion groups . While the class of -groups is contained in the class of -groups, it is in general undecidable in ZFC if the two classes coincide. In this paper we study the endomorphism rings of -groups which are not -groups working in a model of ZFC that satisfies .

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Additional Information

**Lutz Strüngmann**

Affiliation:
Department of Mathematics, University of Duisburg-Essen, Campus Essen, 45117 Essen, Germany

Email:
lutz.struengmann@uni-due.de

DOI:
https://doi.org/10.1090/S0002-9939-09-09954-7

Received by editor(s):
November 24, 2008

Received by editor(s) in revised form:
March 3, 2009

Published electronically:
June 15, 2009

Additional Notes:
The author was supported by a grant from the German Research Foundation DFG

Communicated by:
Julia Knight

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.