Abstract
AbstractA 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 \(3_{+}^{2+1}\).KeywordsDefect GroupFinite Simple GroupsProper SubgroupNilpotent BlockQuasisimple GroupsThese 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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