Defect 3 Blocks of Symmetric Group Algebras

Abstract

Abstract In this paper, we study if the following properties are present in defect 3 blocks of symmetric group algebras k G n , 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 k G n to inherit these properties from a defect 3 block B of k G n − 1 , with which it forms a [3 : 1]-pair. We also verify that the principal blocks of k G n (3 p ≤ n ≤ 4 p − 1) have these properties.