JournalsggdVol. 1 , No. 4DOI 10.4171/ggd/20

On kernels of cellular covers

  • Emmanuel D. Farjoun

    Hebrew University, Jerusalem, Israel
  • Rüdiger Göbel

    Universität Duisburg-Essen, Germany
  • Yoav Segev

    Ben-Gurion University, Beer-Sheva, Israel
  • Saharon Shelah

    The Hebrew University of Jerusalem, Israel
On kernels of cellular covers cover

Abstract

In the present paper we continue to examine cellular covers of groups, focusing on the cardinality and the structure of the kernel K of the cellular map G → M. We show that in general a torsion free reduced abelian group M may have a proper class of non-isomorphic cellular covers. In other words, the cardinality of the kernels is unbounded. In the opposite direction we show that if the kernel of a cellular cover of any group M has certain “freeness” properties, then its cardinality is bounded by |M|.