# Cardinality relation between subsets of a group

$G$ is an abelian group, $A$ and $B$ are non empty finite subsets of $G$. Set $A+B := \{a+b\mid a\in A, b\in B\}$ and $H := \mathrm{stab}(A+B)=\{g\in G \mid g+A+B = A+B\}$.

Prove that $$|A+B|\ge|A+H|+|B+H|-|H|$$ Please help me in finding answer.Thank you in advance

-
Welcome to maths.SE. May I encourage you to edit your question to describe where this problem has come from and where exactly you are stuck? –  Douglas S. Stones May 6 '13 at 17:52
You should look up Kneser's Theorem and realize that there's a good reason as to why you couldn't solve this problem right away. –  Nonoffensive name Aug 1 '13 at 21:55
Here is the shortest proof I've found arxiv.org/pdf/1303.3539v1.pdf –  Nonoffensive name Aug 1 '13 at 22:00