Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 151-173 (2007)
The possibility of extending factorization results to infinite abelian groups
Arthur D. Sands and Sándor SzabóDepartment of Mathematics, University of Dundee, Dundee DD1 4HN Scotland UK; Institute of Mathematics and Informatics, University of Pécs, Ifjúság u. 6, 7624 Pécs, Hungary
Abstract: We shall 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 shall obtain families of infinite abelian groups to which these results cannot be extended. We shall then describe classes of infinite abelian groups for which the extension does hold.
Keywords: factorization of finite and infinite abelian groups, Hajós-Rédei theory.
Classification (MSC2000): 20K99; 52C22
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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.