Restricted Sumsets in Finite Nilpotent Groups
Du, Shanshan, Hao Pan · arXiv (Cornell University) · 2012
Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A ot=B$, then the cardinality of the restricted sumset $$A\dotplus B={a+b: a\in A, b\in B, a eq b} $$ is at least $$\min{p(G),|A|+|B|-2},$$ where $p(G)$ denotes the least prime factor of $|G|$.