On the cardinality of sumsets in torsion-free groups

Károly J. Böröczky, Péter P. Pálfy, Oriol Serra

Let $A,B$ be finite subsets of a torsion-free group $G$. We prove that for every positive integer $k$ there is a $c(k)$ such that if $|B|\ge c(k)$ then the inequality $|AB|\ge |A|…