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The possibility of extending factorization results to infinite Abelian groups. (English) Zbl 1167.20031

Summary: We consider three results on factoring finite Abelian groups by subsets. These are the Hajós’, Rédei’s and simulation theorems. As L. Fuchs has done in the case of Hajós’ theorem we obtain families of infinite Abelian groups to which these results cannot be extended. We then describe classes of infinite Abelian groups for which the extension does hold.

MSC:

20K99 Abelian groups
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
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