Bounding the number of characters in a block of a finite group

We present a strong upper bound on the number k(B) of irreducible characters of a p-block B of a finite group G in terms of local invariants. More precisely, the bound depends on a chosen major B-subsection (u,b), its normalizer NG(〈u〉,b) in the fusion system and a weighted sum of the Cartan invaria...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2019-12, Vol.358, p.106861, Article 106861
Main Author: Sambale, Benjamin
Format: Article
Language:English
Subjects:
Brauer's [formula omitted]-Conjecture
Cartan matrix
Number of characters in a block
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Summary:We present a strong upper bound on the number k(B) of irreducible characters of a p-block B of a finite group G in terms of local invariants. More precisely, the bound depends on a chosen major B-subsection (u,b), its normalizer NG(〈u〉,b) in the fusion system and a weighted sum of the Cartan invariants of b. In this way we strengthen and unify previous bounds given by Brauer, Wada, Külshammer–Wada, Héthelyi–Külshammer–Sambale and the present author.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2019.106861