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

Abstract

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.