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Restricted Sumsets in Finite Nilpotent Groups
Published 27 Jun 2012 in math.CO, math.GR, and math.NT | (1206.6160v6)
Abstract: Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A\not=B$, then the cardinality of the restricted sumset $$A\dotplus B={a+b: a\in A, b\in B, a\neq b} $$ is at least $$\min{p(G),|A|+|B|-2},$$ where $p(G)$ denotes the least prime factor of $|G|$.
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