A short proof of Kneser's addition theorem for abelian groups

Martin Kneser proved the following addition theorem for every abelian group $G$. If $A,B \subseteq G$ are finite and nonempty, then $|A+B| \ge |A+K| + |B+K| - |K|$ where $K = \{g \in G \mid g+A+B = A+B \}$. Here we give a short proof of this based on a simple intersection union argument.Comment: 3 page

Informatique quantique : algorithmes et complexité de la communication

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal