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Almost disjoint abelian groups

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Abstract

Under various set-theoretic hypotheses we construct families of maximal possible size of almost free abelian groups which are pairwise almost disjoint, i.e. there is no non-free subgroup embeddable in two of them. We show that quotient-equivalent groups cannot be almost disjoint, but we show how to construct maximal size families of quotient-equivalent groups of cardinality ℵ1, which are mutually non-embeddable.

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Author notes

  1. P. C. Eklof

    Present address: Department of Mathematics, University of California, 92717, Irvine, CA, USA

  2. A. H. Mekler

    Present address: Department of Mathematics, Simon Fraser University, V5A 1S6, Burnaby, British Columbia, Canada

  3. S. Shelah

    Present address: Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

Authors and Affiliations

  1. Institute for Advanced Studies, The Hebrew University of Jerusalem, Jerusalem, Israel

    P. C. Eklof, A. H. Mekler & S. Shelah

Authors
  1. P. C. Eklof
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  2. A. H. Mekler
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  3. S. Shelah
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Additional information

Dedicated to the memory of Abraham Robinson on the tenth anniversary of this death

First and third authors acknowledge assistance from the US-Israel Binational Science Foundation, Grant No. 1110. First author partially supported by NSF Grant No. MCS-8003691. Second author acknowledges support from the National Science and Engineering Research Council of Canada, Grant No. U0075

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Eklof, P.C., Mekler, A.H. & Shelah, S. Almost disjoint abelian groups. Israel J. Math. 49, 34–54 (1984). https://doi.org/10.1007/BF02760645

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  • DOI: https://doi.org/10.1007/BF02760645

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