2 problems

Let $A\subseteq\mathbb{F}_2^n$ have doubling constant $K$, meaning that $|A+A|\leq K|A|$. A Freiman–Ruzsa theorem says that $A$ can be covered by $F(K)$ translates of a subspace…

Let $F(r,K)$ denote the smallest bound such that, for every abelian group $G$ in which every element has order at most $r$, every finite subset $A\subseteq G$ satisfying…