The sum-capture problem for abelian groups

John P Steinberger

Let $G$ be a finite abelian group, let $0<\alpha <1$, and let $A\subseteq G$ be a random set of size $|G{|}^{\alpha }$. We let $$ μ(A) = \max_{B,C:|B|=|C|=|A|}|\{(a,b,c) \in A \times B \times…