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Blocks with Few Characters

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Blocks of Finite Groups and Their Invariants

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

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Abstract

In this chapter we consider an inverse problem: If the number of irreducible characters in a block is given, what can be said about the defect groups? This question is motivated by Brauer’s Problem 21 which states that there should be only finitely many choices for the defect groups. Extending results by Brauer, Brandt, Külshammer and Chlebowitz, we consider blocks with exactly three irreducible characters. This leads to a classification problem of fusion systems. The proof makes use of the classification of the finite simple groups.

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Authors and Affiliations

  1. Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Germany

    Benjamin Sambale

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  1. Benjamin Sambale
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Sambale, B. (2014). Blocks with Few Characters. 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_15

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