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The Quarterly Journal of Mathematics Advance Access published online on June 10, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han012
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

LARGE INDECOMPOSABLE MINIMAL GROUPS

Saharon Shelah {ddagger}

Department of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel, and Rutgers University, Newbrunswick, NJ, USA

Lutz Strüngmann{dagger}

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

{dagger} Corresponding author. E-mail: Shelah{at}math.huji.ac.il

Received 16 November 2007; revised 24 January 2008
  Abstract

Assuming V=L we prove that there exist indecomposable almost-free minimal groups of size {lambda} for every regular cardinal {lambda} below the first weakly compact cardinal. This is to say that there are indecomposable almost-free torsion-free abelian groups of cardinality {lambda} which are isomorphic to all of their finite index subgroups.

{ddagger} E-mail: lutz.strungmann{at}uni-due.de


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