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Abelian Defect Groups

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2127)

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.

Keywords

  • Abelian Defect Group
  • Inertia Index
  • Regular Orbits
  • Coprime Action
  • Irreducible Characters

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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