A 3-local characterization of \(Fi_{24}'\).
type: Item
instance of: scholarly article
title: A 3-local characterization of \(Fi_{24}'\).
zbMATH Open document ID: 1213.20013
author: M. Reza Salarian
published in: Journal of Algebra
publication date: 2011-01-21T00:00:00Z
review text: A characterization of the third Fischer group \(Fi'_{24}\) by the structure of the centralizer of a 3-central element is given. As a corollary this group is identified from two of its 3-locals. This corollary has application in the ongoing project of \textit{U. Meierfrankenfeld, B. Stellmacher} and \textit{G. Stroth} to classify the groups of local characteristic \(p\) [Groups, combinatorics and geometry. Proceedings of the L.M.S. Durham symposium, Durham, 2001. River Edge, NJ: World Scientific. 155-192 (2003; Zbl 1031.20008)]. Also the corollary has played a crucial role in the paper by the author and \textit{G. Stroth} [J. Algebra 323, No. 4, 1186-1195 (2010; Zbl 1195.20015)] for identifying the Monster from two of its 3-locals.
reviewed by: Anatoli Kondrat'ev
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 5840421
zbMATH Keywords: finite simple groups
zbMATH Keywords: sporadic groups
zbMATH Keywords: 3-local subgroups
zbMATH Keywords: Fischer groups
zbMATH Keywords: 3-local characterizations
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.08.012
OpenAlex ID: W2029366169
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DOI: 10.1016/J.JALGEBRA.2010.08.012
description: scientific article; zbMATH DE number 5840421