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Minimal Non-abelian 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

A finite group is called minimal non-abelian if all its proper subgroups are abelian, but the whole group is not. In this chapter we describe all 2-blocks with minimal non-abelian defect groups. As a special feature we are able to verify Donovan’s Conjecture of one infinite family of defect groups. The proof makes use of the classification of the finite simple groups. For odd primes we prove that Olsson’s Conjecture holds for blocks with minimal non-abelian defect groups except perhaps for the extraspecial group \(3_{+}^{2+1}\).

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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). Minimal Non-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_12

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