Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On endomorphism rings of $B_1$-groups that are not $B_2$-groups
HTML articles powered by AMS MathViewer

by Lutz Strüngmann
Proc. Amer. Math. Soc. 137 (2009), 3657-3668
DOI: https://doi.org/10.1090/S0002-9939-09-09954-7
Published electronically: June 15, 2009

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 $B_2$-group $G$ is a union of an ascending chain of pure subgroups $G_{\alpha }$ such that for every $\alpha$ we have $G_{\alpha +1}=G_{\alpha }+H_{\alpha }$ for some finite rank Butler group $H_{\alpha }$. A $B_1$-group is a torsion-free group $G$ satisfying $\mathrm {Bext}_{\mathbb {Z}}^1(G,T)=0$ for all torsion groups $T$. While the class of $B_2$-groups is contained in the class of $B_1$-groups, it is in general undecidable in ZFC if the two classes coincide. In this paper we study the endomorphism rings of $B_1$-groups which are not $B_2$-groups working in a model of ZFC that satisfies $2^{\aleph _0}=\aleph _4$.
References
Similar Articles
Bibliographic Information
  • Lutz Strüngmann
  • Affiliation: Department of Mathematics, University of Duisburg-Essen, Campus Essen, 45117 Essen, Germany
  • Email: lutz.struengmann@uni-due.de
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 3657-3668
  • MSC (2000): Primary 20K15, 20K20, 20K35, 20K40; Secondary 18E99, 20J05
  • DOI: https://doi.org/10.1090/S0002-9939-09-09954-7
  • MathSciNet review: 2529872