Defect 3 blocks of symmetric group algebras, I

Abstract

In this paper, we study if the following properties are present in defect 3 blocks of symmetric group algebras kGn, where k has characteristic p (≥5): the Ext-quiver is bipartite; the p.i.m.'s have a common Loewy length 7.We obtain a criteria for a defect 3 block B of kGn to inherit these properties from a defect 3 block B̃ of kGn-1, with which it forms a [3:1]-pair. We also verify that the principal blocks of kGn (3p≤n≤4p-1) have these properties. © 2001 Academic Press.