# Rank of sumsets in matroids

Assume that $$G$$ is a (finite) abelian group and $$M$$ is a matroid whose ground set is G. Let $$X$$ and $$Y$$ be subsets of G, and $$H$$ is the stabilizer of $$X+Y$$. That is $$X+Y+H$$=$$X+Y$$. We denote the rank function of $$M$$ by $$r$$. Then can we say that $$r(X+Y)geq$$ $$r(X)+r(Y)-r(H)$$?
(A similar result holds for the cardinality of sumsets of a given group, well-known as Kneser’s theorem)