The Alperin and Dade conjectures for the Conway simple group \(Co_1\).
type: Item
instance of: scholarly article
title: The Alperin and Dade conjectures for the Conway simple group \(Co_1\).
zbMATH Open document ID: 1053.20009
DOI: 10.1023/B:ALGE.0000026809.78997.19
author: Jianbei An
author: E. A. O'Brien
published in: Algebras and Representation Theory
publication date: 2004-08-19T00:00:00Z
review text: The authors continue their mission to verify the Alperin and Dade conjectures for all the sporadic simple groups. These deep conjectures relate the numbers of ordinary irreducible characters of given defect in a finite group to corresponding numbers in certain local subgroups, via an alternating sum formula. The verification comes in two parts: first a detailed analysis of the maximal local subgroups reveals which local subgroups need to be studied, and then their character tables are computed, so that the numbers of characters with the required properties can be read off. In this paper the local analysis is presented in full, and the character calculations are very sensibly suppressed -- a webpage with more details is provided for those who are interested.
Mathematics Subject Classification ID: 20C34
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 2093329
zbMATH Keywords: weights
zbMATH Keywords: blocks
zbMATH Keywords: Alperin conjecture
zbMATH Keywords: radical subgroups
zbMATH Keywords: radical chains
zbMATH Keywords: Dade conjectures
zbMATH Keywords: numbers of characters
zbMATH Keywords: character tables
reviewed by: Robert A. Wilson
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: b:alge.0000026809.78997.19
OpenAlex ID: W1979626159
description: scientific article; zbMATH DE number 2093329