Abstract
In this chapter, we prove two very basic results concerning finite sumsets over a torsion-free abelian group. First, we show that any finite sumset over a torsion-free abelian group is isomorphic to a sumset over the integers. Second, we give the basic lower bound for finite sumsets over a torsion-free group, including characterizing the case of equality.
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References
M.B. Nathanson, Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Springer, Harrisonburg, 1996)
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© 2013 Springer International Publishing Switzerland
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Grynkiewicz, D.J. (2013). Simple Results for Torsion-Free Abelian Groups. In: Structural Additive Theory. Developments in Mathematics, vol 30. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00416-7_3
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DOI: https://doi.org/10.1007/978-3-319-00416-7_3
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00415-0
Online ISBN: 978-3-319-00416-7
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