A note on the number of irreducible characters in a p-block with normal defect group
type: Item
instance of: scholarly article
title: A note on the number of irreducible characters in a p-block with normal defect group
zbMATH Open document ID: 0544.20009
author: Masafumi Murai
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: In a previous paper [Osaka J. Math. 21, 387-398 (1984; Zbl 0538.20007)] the author had proved that for a finite p-solvable group the number of irreducible characters in a p-block is bounded by the order of its defect group D provided that p is large compared with the sectional rank of D, a special case of Brauer's conjecture. In this short note he applies this to prove the analogous result for blocks with normal defect group in an arbitrary finite group. The proof could have been even shorter by referring to a result of \textit{W. F. Reynolds} on the structure of blocks with normal defect groups [Nagoya Math. J. 22, 15-32 (1963; Zbl 0131.263)].
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 3865547
zbMATH Keywords: finite p-solvable group
zbMATH Keywords: number of irreducible characters
zbMATH Keywords: sectional rank
zbMATH Keywords: Brauer's conjecture
zbMATH Keywords: blocks
zbMATH Keywords: normal defect groups
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: pjaa.59.488
OpenAlex ID: W1989351479
cites work: Q3236698
cites work: Q3955560
cites work: Group Characters and Normal Hall Subgroups
cites work: The number of conjugacy classes in a finite group
cites work: A note on the number of irreducible characters in a p-block of a finite group
DOI: 10.3792/PJAA.59.488
description: scientific article; zbMATH DE number 3865547