2-radical subgroups of the Conway simple group \(Co_1\)
type: Item
instance of: scholarly article
title: 2-radical subgroups of the Conway simple group \(Co_1\)
zbMATH Open document ID: 0917.20013
author: Masato Sawabe
published in: Journal of Algebra
publication date: 1999-07-06T00:00:00Z
review text: A \(p\)-subgroup of a group \(G\) is called \(p\)-radical if it is the largest normal \(p\)-subgroup of its normalizer. These subgroups are the important ones for calculating the \(\text{mod }p\) cohomology, and for verifying Dade's conjecture, which refers to chains of \(p\)-radical subgroups. The present paper uses the list of maximal 2-local subgroups of Conway's group \(Co_1\), determined by \textit{R. T. Curtis} [J. Algebra 63, 413-434 (1980; Zbl 0427.20010)], to classify the conjugacy classes of 2-radical subgroups of \(Co_1\). It turns out that there are 30 of them.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 1251297
zbMATH Keywords: chains of \(p\)-radical subgroups
zbMATH Keywords: maximal 2-local subgroups
zbMATH Keywords: Conway group \(Co_1\)
zbMATH Keywords: conjugacy classes
reviewed by: Robert A. Wilson
MaRDI profile type: Publication
full work available at URL: jabr.1998.7573
OpenAlex ID: W2054058162
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DOI: 10.1006/JABR.1998.7573
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description: scientific article; zbMATH DE number 1251297