Geodesic
On kernels of cellular covers
Emmanuel D. Farjoun1 ; Rüdiger Göbel2 ; Yoav Segev3 ; Saharon Shelah4 orcid
1Hebrew University, Jerusalem, Israel
2Universität Duisburg-Essen, Germany
3Ben-Gurion University, Beer-Sheva, Israel
4The Hebrew University of Jerusalem, Israel
Groups, geometry, and dynamics, Tome 1 (2007) no. 4, pp. 409-419

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DOI

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∣.
DOI : 10.4171/ggd/20
Classification : 20-XX, 00-XX
Mots-clés : Cellular cover, infinite cardinal, free abelian group

Emmanuel D. Farjoun  1   ; Rüdiger Göbel  2   ; Yoav Segev  3   ; Saharon Shelah  4

1 Hebrew University, Jerusalem, Israel
2 Universität Duisburg-Essen, Germany
3 Ben-Gurion University, Beer-Sheva, Israel
4 The Hebrew University of Jerusalem, Israel 
Emmanuel D. Farjoun; Rüdiger Göbel; Yoav Segev; Saharon Shelah. On kernels of cellular covers. Groups, geometry, and dynamics, Tome 1 (2007) no. 4, pp. 409-419. doi: 10.4171/ggd/20
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