Lower defect groups in symmetric groups (Q1083531)

Multiplicities of lower defect groups, as introduced by R. Brauer, are important invariants of a block. For example, they can be used to compute the numbers of irreducible ordinary and modular characters and the elementary divisors of its Cartan matrix. The main purpose of the paper under review is to give a combinatorial description of these multiplicities for blocks of symmetric groups. In addition, the author presents a brief and elegant introduction (with proofs) into the block theory of symmetric groups, including the so-called Nakayama conjecture and a list of subpairs.