On the Inductive Alperin–mckay and Alperin Weight Conjecture for Groups with Abelian Sylow Subgroups
نویسنده
چکیده
We study the inductive Alperin–McKay conjecture, the inductive Isaacs– Navarro refinement and the inductive blockwise Alperin weight conjecture for groups of Lie type in the generic case of abelian Sylow `-subgroups. We also show that the alternating groups, the Suzuki groups and the Ree groups satisfy the inductive condition necessary for Späth’s reduction of the blockwise Alperin weight conjecture to the case of simple groups.
منابع مشابه
New refinements of the McKay conjecture for arbitrary finite groups
Let G be an arbitrary finite group and fix a prime number p. The McKay conjecture asserts that G and the normalizer in G of a Sylow p-subgroup have equal numbers of irreducible characters with degrees not divisible by p. The Alperin-McKay conjecture is version of this as applied to individual Brauer p-blocks of G. We offer evidence that perhaps much stronger forms of both of these conjectures a...
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