A note on Olsson始s Conjecture

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• 作者：L谩szlo H茅thelyi ; Burkhard K眉lshammer ; Benjamin Sambale
• 关键词：Block ; Characters ; Height ; p-Rank ; Defect group ; Subsection
• 刊名：Journal of Algebra
• 出版年：15 January, 2014
• 年：2014
• 卷：398
• 期：Complete
• 页码：364-385
• 全文大小：350 K

文摘

For a p-block B of a finite group G with defect group D Olsson conjectured that , where is the number of characters in B of height 0 and denotes the commutator subgroup of D. Brauer deduced Olsson始s Conjecture in the case where D is a dihedral 2-group using the fact that certain algebraically conjugate subsections are also conjugate in G. We generalize Brauer始s argument for arbitrary primes p and arbitrary defect groups. This extends two results by Robinson. For we show that Olsson始s Conjecture is satisfied for defect groups of p-rank 2 and for minimal non-abelian defect groups.