Britta Späth

A reduction theorem for the Alperin–McKay conjecture

Abstract As a first step in a general verification of the Alperin–McKay conjecture, we prove a reduction of the conjecture to statements about simple groups. Furthermore we show in numerous cases, that simple groups satisfy the required conditions. The methods are also applied to obtain similar results for refinements due to Isaacs and Navarro.

On Brauer’s Height Zero Conjecture

In this paper, the unproven half of Richard Brauer’s Height Zero Conjecture is reduced to a question on simple groups.

The inductive Alperin–McKay and Blockwise Alperin Weightconditions for blocks with cyclic defect groups and odd primes

Abstract We verify the inductive Blockwise Alperin Weight (BAW) and the inductive Alperin–McKay (AM) conditions introduced by the second author, for p-blocks of finite quasisimple groups with cyclic defect groups whenever the prime p is odd. Furthermore, we establish a criterion that describes conditions under which the inductive AM condition for blocks with abelian defect groups implies the inductive BAW condition for those blocks.