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


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|.

Cite this article

Emmanuel D. Farjoun, Rüdiger Göbel, Yoav Segev, Saharon Shelah, On kernels of cellular covers. Groups Geom. Dyn. 1 (2007), no. 4, pp. 409–419

DOI 10.4171/GGD/20