Saturation on Locally Compact Abelian Groups: An Extended Theorem.
Walter Schempp, Bernd Dreseler (1973)
Manuscripta mathematica
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Saturation on Locally Compact Abelian Groups: An Extended Theorem.
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We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic...
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