  We study the multiplicities of Young modules as direct summands of
permutation modules on cosets of Young subgroups. Such multiplicities have
become known as the p-Kostka numbers. We classify the indecomposable Young
permutation modules, and, applying the Brauer construction for p-permutation
modules, we give some new reductions for p-Kostka numbers. In particular we
prove that p-Kostka numbers are preserved under multiplying partitions by p,
and strengthen a known reduction given by Henke, corresponding to adding
multiples of a p-power to the first row of a partition.
