Additive Bases in Abelian Groups

Vsevolod F. Lev, Mikhail E. Muzychuk, Rom Pinchasi

Let $G$ be a finite, non-trivial abelian group of exponent $m$, and suppose that $B_1,...,B_k$ are generating subsets of $G$. We prove that if $k>2m\ln {\log }_2|G|$, then the mul…