Cartan matrices and Brauer's \(k(B)\)-conjecture. II.
type: Item
instance of: scholarly article
title: Cartan matrices and Brauer's \(k(B)\)-conjecture. II.
zbMATH Open document ID: 1243.20013
author: Benjamin Sambale
published in: Journal of Algebra
publication date: 2012-01-11T00:00:00Z
review text: This paper continues the author's earlier work in part I [\textit{B. Sambale}, J. Algebra 331, No. 1, 416-427 (2011; Zbl 1230.20010)] and uses this to obtain some more results on Brauer's \(k(B)\)-conjecture. In particular, this conjecture is proved if the defect group contains a central, cyclic subgroup of index at most 9. As a consequence, the conjecture holds for 3-blocks of defect at most 3. It is also shown that the \(k(B)\)-conjecture holds for 2-blocks of defect 5 except possibly the central product of \(D_8\) by itself. (This work ultimately depends on CFSG.) There is also a discussion of an example illustrating the limits of the methods used in the paper. Some proofs are computational in nature and depend on calculations performed with GAP.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C40
zbMATH DE Number: 5996447
zbMATH Keywords: Cartan matrices
zbMATH Keywords: Brauer \(k(B)\)-conjecture
zbMATH Keywords: minimal nonmetacyclic defect groups
zbMATH Keywords: numbers of irreducible Brauer characters
zbMATH Keywords: numbers of ordinary irreducible characters
Wikidata QID: Q58940474
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.03.023
OpenAlex ID: W203857977
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DOI: 10.1016/J.JALGEBRA.2011.03.023
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description: scientific article; zbMATH DE number 5996447