Proof of a conjecture of Green and Liebeck on codes in symmetric groups

Teng Fang, Jinbao Li

Let $A$ and $B$ be subsets of a finite group $G$ and $r$ a positive integer. If for every $g\in G$, there are precisely $r$ pairs $(a,b)\in A\times B$ such that $g=ab$, then $B$ is…