Geodesic
Quasi-isolated blocks and the Alperin–McKay conjecture
Forum of Mathematics, Sigma, Tome 10 (2022)

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The 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. 
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     author = {Lucas Ruhstorfer},
     title = {Quasi-isolated blocks and the {Alperin{\textendash}McKay} conjecture},
     journal = {Forum of Mathematics, Sigma},
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Lucas Ruhstorfer. Quasi-isolated blocks and the Alperin–McKay conjecture. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.36

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