Abstract
AbstractThe Alperin–McKay conjecture is a longstanding open conjecture in the representation theory of finite groups. Späth showed that the Alperin–McKay conjecture holds if the so-called inductive Alperin–McKay (iAM) condition holds for all finite simple groups. In a previous paper, the author has proved that it is enough to verify the inductive condition for quasi-isolated blocks of groups of Lie type. In this paper, we show that the verification of the iAM-condition can be further reduced in many cases to isolated blocks. As a consequence of this, we obtain a proof of the Alperin–McKay conjecture for$2$-blocks of finite groups with abelian defect.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
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