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Small Defect Groups

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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

We use the results from the previous chapters in order to gain complete information about blocks with small defect groups. We also make use of the Cartan method. As an outcome, we give a complete description of the 2-blocks of defect at most 4. Additionally, we investigate some of the defect groups of order 32. The main result shows that Brauer’s k(B)-Conjecture and Olsson’s Conjecture are true for every 2-block of defect at most 5. The former conjecture is also verified for the defect groups of order 27. Finally, we are able to classify all 2-blocks with minimal non-metacyclic defect groups.

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  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). Small 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_13

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