Abstract
A result by Brauer and Feit bounds the number of irreducible characters in a block by the square of the order of the defect group. We improve this bound for blocks with abelian defect groups. The proof uses results about regular orbits under coprime actions. Moreover, we show that Brauer’s k(B)-Conjecture holds for blocks with abelian defect groups if the inertial index is less than 256.
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Sambale, B. (2014). Abelian Defect Groups. In: Blocks of Finite Groups and Their Invariants. Lecture Notes in Mathematics, vol 2127. Springer, Cham. https://doi.org/10.1007/978-3-319-12006-5_14
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DOI: https://doi.org/10.1007/978-3-319-12006-5_14
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