Cohomology of the double cover of the Mathieu group \(M_{12}\)
type: Item
instance of: scholarly article
title: Cohomology of the double cover of the Mathieu group \(M_{12}\)
zbMATH Open document ID: 0953.20042
published in: Journal of Algebra
publication date: 2000-10-24T00:00:00Z
review text: \textit{A. Adem, J. Maginnis} and \textit{R. J. Milgram} [J. Algebra 139, No. 1, 90-133 (1991; Zbl 0743.20052)] have calculated the mod two cohomology \(H^*(M_{12},F_2)\) of the Mathieu group \(M_{12}\). In this paper, the mod two cohomology of the double cover \(2M_{12}\) of \(M_{12}\) is calculated. The authors use a hypercohomology spectral sequence to determine a differential in the Lyndon-Hochschild-Serre spectral sequence of the central extension. Ungrading the \(E_\infty\) page of the Lyndon-Hochschild-Serre spectral sequence involves recourse to some computer calculations using the MAGMA computer algebra package. The programs are designed only for computing with \(p\)-groups, so this involves restrictions to a Sylow 2-subgroup of \(2M_{12}\).
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 1441823
zbMATH Keywords: cohomology of finite groups
zbMATH Keywords: sporadic Mathieu group \(M_{12}\)
zbMATH Keywords: double covers
zbMATH Keywords: spectral sequences
author: David Benson
author: Jon F. Carlson
reviewed by: Anatoli Kondrat'ev
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: jabr.1999.8207
OpenAlex ID: W2037421808
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DOI: 10.1006/JABR.1999.8207
description: scientific article; zbMATH DE number 1441823