In this paper we study the modular structure of the permutation module H-(2n) of the symmetric group S-2n, acting on set partitions of a set of size 2n into n sets each of size 2, defined over a field of odd characteristic p. In particular we characterise the vertices of the indecomposable summands of H-(2n) and fully describe all of its indecomposable summands that lie in blocks of p-weight at most two. When 2n < 3p we show that there is a unique summand of H-(2n) in the principal block of S-2n and that this summand exhibits many of the extensions between simple modules in its block. (C) 2016 Elsevier B.V. All rights reserved.
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