  The maximal dimension of a commutative subalgebra of the Grassmann algebra is
determined. It is shown that for any commutative subalgebra there exists a
commutative subalgebra which is spanned by monomials and has the same
dimension. It follows that the maximal dimension of a commutative subalgebra
can be expressed in terms of the maximal size of an intersecting system of
subsets of odd size in a finite set.
