On Olsson's conjecture for blocks with metacyclic defect groups of odd order.
type: Item
instance of: scholarly article
title: On Olsson's conjecture for blocks with metacyclic defect groups of odd order.
zbMATH Open document ID: 1227.20004
author: Sheng Yang
published in: Archiv der Mathematik
publication date: 2011-06-17T00:00:00Z
review text: A 1984 conjecture of Olsson states that if \(G\) is a finite group, \(p\) a prime and \(B\) a \(p\)-block of \(G\) with defect group \(D\), then the number of ordinary irreducible characters of height 0 in \(B\) is bounded above by \(|D:D'|\). In the paper under review, the author proves this conjecture in the case that \(D\) is metacyclic. To establish the result, the author can focus on the case that \(p\) is odd, since the even case has been resolved recently by \textit{B. Sambale} [Fusion systems on metacyclic 2-groups. \url{arXiv:0908.0783}].
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 5909098
zbMATH Keywords: Olsson conjecture
zbMATH Keywords: blocks
zbMATH Keywords: defect groups
zbMATH Keywords: metacyclic groups
zbMATH Keywords: numbers of irreducible characters
MaRDI profile type: Publication
Wikidata QID: Q123231162
full work available at URL: s00013-011-0251-4
OpenAlex ID: W2006298865
cites work: Local methods in block theory
cites work: On the Arithmetic in a Group Ring
cites work: A Frobenius theorem for blocks
cites work: Blocks with cyclic defect groups
cites work: Stable splittings of classifying spaces of metacyclic \(p\)-groups, \(p\) odd
cites work: Q3955560
cites work: On the Number of Ordinary Irreducible Characters in ap-Block with a Minimal Nonabelian Defect Group
cites work: On Brauer's \(k(B)\)-problem for blocks with metacyclic defect groups of odd order.
cites work: Q3913574
cites work: Q3826736
cites work: On 2-blocks with quaternion and quasihedral defect groups
cites work: On subpairs and modular representation theory
cites work: On the number of characters in blocks of finite general linear, unitary and symmetric groups
cites work: On Brauer's \(k(B)\)-problem
cites work: Further consequences of conjectures like Alperin's
cites work: Fusion systems on metacyclic 2-groups.
cites work: The \(\text{mod }p\) cohomology algebras of finite groups with metacyclic Sylow \(p\)-subgroups
cites work: CONTROL OF FUSION IN FUSION SYSTEMS
cites work: On the control of fusion in the local category for the \(p\)-block with a minimal nonabelian defect group.
DOI: 10.1007/S00013-011-0251-4
Recommended article: On Brauer's \(k(B)\)-problem for blocks with metacyclic defect groups of odd order.
Recommended article: Blocks of full defect with nonabelian metacyclic defect groups.
Recommended article: Isotypies for \(p\)-blocks with non-abelian metacyclic defect groups, \(p\) odd
Recommended article: ON BLOCKS WITH CYCLIC DEFECT GROUPS AND THEIR HEAD ORDERS
Recommended article: Donovan’s conjecture and blocks with abelian defect groups
Recommended article: A note on blocks with dihedral defect groups.
Recommended article: Blocks with extraspecial defect groups of finite quasisimple groups.
Recommended article: A note on blocks with Abelian defect groups.
Recommended article: On defect groups for generalized blocks of the symmetric group
Recommended article: Q4316824
description: scientific article; zbMATH DE number 5909098