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. 409–419DOI 10.4171/GGD/20