Mathematical Notes

, Volume 103, Issue 1–2, pp 271–289 | Cite as

On Two-Dimensional Sums in Abelian Groups



It is proved that if, for a subset A of a finite Abelian group G, under the action of a linear operator L: G3G2, the image L(A, A, A) has cardinality less than (7/4)|A|2, then there exists a subgroup HG and an element xG for which AH + x; further, |H| < (3/2)|A|.


Abelian group linear operator convolution sums of sets additive combinatorics 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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