We prove that if $G$ is an Abelian group and $A_1,\ldots,A_k \subseteq G$ satisfy $m A_i=G$ (the $m$-fold sumset), then $A_1+\cdots+A_k=G$ provided that $k \ge c_m \log \log |G|$. This generalizes a result of Alon, Linial, and Meshulam [Additive bases of vector spaces over prime fields. J. Combin. Theory Ser. A, 57(2):203—210, 1991] regarding so-called additive bases.
@article{10_37236_6276,
author = {Victoria de Quehen and Hamed Hatami},
title = {On the additive bases problem in finite fields},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {3},
doi = {10.37236/6276},
zbl = {1348.11009},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6276/}
}
TY - JOUR
AU - Victoria de Quehen
AU - Hamed Hatami
TI - On the additive bases problem in finite fields
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6276/
DO - 10.37236/6276
ID - 10_37236_6276
ER -
%0 Journal Article
%A Victoria de Quehen
%A Hamed Hatami
%T On the additive bases problem in finite fields
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6276/
%R 10.37236/6276
%F 10_37236_6276
Victoria de Quehen; Hamed Hatami. On the additive bases problem in finite fields. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/6276
