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. 
@article{DM_2018_30_4_a8,
     author = {A. A. Sapozhenko and V. G. Sargsyan},
     title = {The number of sumsets in {Abelian} group},
     journal = {Diskretnaya Matematika},
     pages = {96--105},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_4_a8/}
}
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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/