Defect 3 Blocks of Symmetric Group Algebras, I,

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