Groups, Geometry, and Dynamics

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Volume 1, Issue 4, 2007, pp. 409–419
DOI: 10.4171/GGD/20

Published online: 2007-12-31

On kernels of cellular covers

Emmanuel D. Farjoun[1], Rüdiger Göbel, Yoav Segev[2] and Saharon Shelah[3]

(1) Hebrew University, Jerusalem, Israel
(2) Ben-Gurion University, Beer-Sheva, Israel
(3) 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|.

Keywords: Cellular cover, infinite cardinal, free abelian group

Farjoun Emmanuel, Göbel Rüdiger, Segev Yoav, Shelah Saharon: On kernels of cellular covers. Groups Geom. Dyn. 1 (2007), 409-419. doi: 10.4171/GGD/20