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Titlebook: Structural Additive Theory; David J. Grynkiewicz Book 2013 Springer International Publishing Switzerland 2013 Abelian groups.Freiman homom

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The DeVos-Goddyn-Mohar Theoremsubsequence sums alongside results for sumsets. Indeed, Kneser’s Theorem is simply one very particular case of the DeVos-Goddyn-Mohar Theorem, and it should later be put in comparison with the Partition Theorem as the two theorems share much overlap though neither one encompasses the entirety of the other.
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The Partition Theorem IIe explored this is more detail. The aim of this chapter is to extend the potency of such conclusions for finite abelian groups by reducing how large . must be and allowing limited weight sequences as well.
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Developments in Mathematicshttp://image.papertrans.cn/s/image/879817.jpg
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https://doi.org/10.1007/978-3-319-00416-7Abelian groups; Freiman homomorphisms; Kneser‘s Theorem; Universal Ambient Group of sumsets; Vosper‘s Th
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Kemperman’s Critical Pair TheoryThe goal of this chapter is to prove one of the most important inverse results for an . abelian group—the Kemperman Structure Theorem (KST)—which determines all finite, nonempty subsets ., .⊆. with |.+.|≤|.|+|.|−1. As the proof is already involved enough for the case when . and . are finite, we only present the result in this case.
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