On p-blocks with Abelian defect groups and inertial index 2 or 3. II
type: Item
instance of: scholarly article
title: On p-blocks with Abelian defect groups and inertial index 2 or 3. II
zbMATH Open document ID: 0675.20006
DOI: 10.1016/0021-8693(89)90239-1
author: Yoko Usami
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let G be a finite group and p a fixed prime number. Let B be a p-block of G with a defect group D. Let l(B) be the number of irreducible Brauer characters in B and k(B) the number of irreducible ordinary characters in B. In case D is abelian with inertial index \(e=2\) or 3 and \(p\neq 2\), we determined l(B) \((=e)\) and k(B) in Part I [ibid. 119, No.1, 123-146 (1988; Zbl 0659.20008)]. In this paper combining the results in [loc. cit.] with a property of a p-rational irreducible character, we determine some generalized decomposition numbers of B in that case. We use the same notations as those in [loc. cit.].
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 4105198
zbMATH Keywords: abelian defect group
zbMATH Keywords: finite group
zbMATH Keywords: p-block
zbMATH Keywords: number of irreducible Brauer characters
zbMATH Keywords: number of irreducible ordinary characters
zbMATH Keywords: inertial index
zbMATH Keywords: p- rational irreducible character
zbMATH Keywords: generalized decomposition numbers
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90239-1
OpenAlex ID: W1979232214
cites work: On the connection between the ordinary and the modular characters of groups of finite order
cites work: Q3955560
cites work: On p-blocks with Abelian defect groups and inertial index 2 or 3. I
cites work: Q3691915
cites work: On generalized decomposition numbers and Fong's reductions
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description: scientific article; zbMATH DE number 4105198