Geodesic
The number of sumsets in Abelian group
Diskretnaya Matematika, Tome 30 (2018) no. 4, pp. 96-105.

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Asymptotic upper and lower bounds for the numbers of distinct subsets $A+B$ in Abelian group of order $n$ are derived, where $|A|,|B|\geq n(\log_{}n)^{-1/8}.$
Keywords: set, characteristic function, group, progression, coset. 
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A. A. Sapozhenko; V. G. Sargsyan. The number of sumsets in Abelian group. Diskretnaya Matematika, Tome 30 (2018) no. 4, pp. 96-105. http://geodesic.mathdoc.fr/item/DM_2018_30_4_a8/

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