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On Brauer’s k(B)-problem for blocks with metacyclic defect groups of odd order

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Abstract

Let G be a finite group, and suppose that B is a p-block of G with defect group D. Let k(B) denote the number of ordinary irreducible characters in B. It was conjectured by Brauer that k(B) ≤ |D|. In this paper, we will prove Brauer’s inequality in the case that D is metacyclic and p is odd.

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  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Sheng Gao

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  1. Sheng Gao
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Correspondence to Sheng Gao.

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Gao, S. On Brauer’s k(B)-problem for blocks with metacyclic defect groups of odd order. Arch. Math. 96, 507–512 (2011). https://doi.org/10.1007/s00013-011-0265-y

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