On the number of irreducible characters in a finite group. II
type: Item
instance of: scholarly article
title: On the number of irreducible characters in a finite group. II
zbMATH Open document ID: 0571.20008
author: Tomoyuki Wada
published in: Hokkaido Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: [Part I, cf. ibid. 12, 74-82 (1983; Zbl 0517.20002).] Let B be a p-block of the finite group G, P a Sylow p-subgroup of G, D a defect group of B, k(B) the number of irreducible complex characters in B and m(B) the number of indecomposable direct summands of the block ideal B considered as a P-module under the conjugation action. The main result of this paper asserts that \(| P:D| k(B)\leq m(B)\) if D is contained in the center of P. Furthermore, the author corrects an error occurring in his earlier paper [ibid. 10, 319-332 (1981; Zbl 0471.20004)].
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 3910597
zbMATH Keywords: p-block
zbMATH Keywords: Sylow p-subgroup
zbMATH Keywords: defect group
zbMATH Keywords: number of irreducible complex characters
zbMATH Keywords: direct summands
zbMATH Keywords: block ideal
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381757658
OpenAlex ID: W2091260589
DOI: 10.14492/HOKMJ/1381757658
description: scientific article; zbMATH DE number 3910597