2007/02/11 by Farjoun, Emmanuel D., Goebel, Ruediger, Segev, Yoav +1
#Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)
paper · doi:10.48550/arxiv.math/0702294
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.