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

Young module multiplicities and classifying the indecomposable Young permutation modules