On the construction of the finite simple groups with a given centralizer of a 2-central involution
type: Item
instance of: scholarly article
title: On the construction of the finite simple groups with a given centralizer of a 2-central involution
zbMATH Open document ID: 0971.20009
author: Gerhard O. Michler
published in: Journal of Algebra
publication date: 2001-10-29T00:00:00Z
review text: The author gives a survey of his programme to construct all the sporadic simple groups in a `uniform' way. It is not entirely uniform, and does not work in all cases, but appears to be designed to plug in to the proof of the classification theorem for finite simple groups. The computations are necessarily hard, as he deliberately avoids using any of the many clever tricks and arguments used in the original constructions. Striving for uniformity has the unfortunate side-effect that the calculations can only be performed by custom-built programs running on massively-parallel machines. The method is to start with an involution centralizer, and to construct a suitable amalgamation of this group with a fours-group normalizer, using the methods developed by Norton, Parker et al. in Cambridge in the 1970s. From this, a permutation representation is made by permuting an orbit of vectors, and the methods of Sims are used to deduce the required properties of the group. Eventually, one has an existence proof for the group in question.
Mathematics Subject Classification ID: 20C40
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 1565882
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: computations
zbMATH Keywords: involution centralizers
zbMATH Keywords: amalgamations
zbMATH Keywords: normalizers
zbMATH Keywords: permutation representations
zbMATH Keywords: existence proofs
reviewed by: Robert A. Wilson
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: jabr.2000.8549
OpenAlex ID: W2087230466
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DOI: 10.1006/JABR.2000.8549
description: scientific article; zbMATH DE number 1565882