On kernels of cellular covers

by Dror Farjoun and Goebel and Segev and Shelah. [FGSSh:892]
Groups, Geometry, and Dynamics, 2007
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 must be bounded.

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