Restricted Sumsets in Finite Nilpotent Groups

Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A≠B$, then the cardinality of the restricted sumset $$A\dotplus B=a+b:a\in A,b\in B,a\mathrm{\ne }b$$ is at least $$\min p(G),\mathrm{\mid }A\mathrm{\mid }+\mathrm{\mid }B\mathrm{\mid }-2,$$ where $p(G)$ denotes the least prime factor of $\mathrm{\mid }G\mathrm{\mid }$.