2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123784In 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.Group TheoryAlgebraic TopologyLogictext