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

Benjamin Sambale

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arXiv · 1807.08238

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

Benjamin Sambale

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Abstract

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 N_G(\langle u\rangle,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, K\"ulshammer--Wada, H\'ethelyi--K\"ulshammer--Sambale and the present author.

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Benjamin Sambale. 2018-07-22. Bounding the number of characters in a block of a finite group. https://arxiv.org/abs/1807.08238

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