A New Proof of Kemperman's Theorem

Abstract

Let $G$ be an additive abelian group and let $A,B\subseteq G$ be finite and nonempty. The pair $(A,B)$ is called critical if the sumset $A+B = {a+b \mid $a \in A$and$b\in B$}$ satisfies $|A+B|<|A|+|B|$. Vosper proved a theorem which characterizes all critical pairs in the special case when $|G|$ is prime. Kemperman generalized this by proving a structure theorem for critical pairs in an arbitrary abelian group. Here we give a new proof of Kemperman's Theorem.

20 pages, 1 figure

References in corpus (1)

• Hyper-atoms and the Kemperman's critical pair Theory