  The Foulkes module H^(a^b) is the permutation module for the symmetric group
S_ab given by the action of S_ab on the collection of set partitions of a set
of size ab into b sets each of size a. The main result of this paper is a
sufficient condition for a simple CS_{ab}-module to have zero multiplicity in
H^(a^b). A special case of this result implies that no Specht module labelled
by a hook partition (ab - r, 1^r) appears in H(a^b).
