A 3-local identification of two almost simple extensions of \(P\Omega_8^+(2)\).
type: Item
instance of: scholarly article
title: A 3-local identification of two almost simple extensions of \(P\Omega_8^+(2)\).
zbMATH Open document ID: 1247.20016
author: Sarah Astill
published in: Journal of Algebra
publication date: 2011-05-16T00:00:00Z
review text: For a prime \(p\), a finite group \(G\) is of parabolic characteristic \(p\) if \(C_H(O_p(H))\leq O_p(H)\) for any \(p\)-local subgroup \(H\) of \(G\) where \(H\) contains a Sylow \(p\)-subgroup of \(G\). There exists a project of the study of groups of parabolic characteristic \(p\) [see \textit{U. Meierfrankenfeld, B. Stellmacher} and \textit{G. Stroth}, in Groups, combinatorics and geometry. Proceedings of the L.M.S. Durham symposium, Durham 2001. River Edge: World Scientific. 155-192 (2003; Zbl 1031.20008)]. The author provides a 3-local characterization of the almost simple groups of parabolic characteristic 3 of shapes \(P\Omega^+_8(2).3\) and \(P\Omega^+_8(2).\text{Sym}(3)\) (the simple group \(P\Omega^+_8(2)\) is not of parabolic characteristic 3). This result is used by \textit{C. Parker} and \textit{G. Stroth} [A characterization of \(^2E_6(2)\), \(Fi_{22}\) and \(\Aut(Fi_{22})\) from a characteristic 3 perspective. Preprint (2010)] for the 3-local characterization of the other such group namely \(^2E_6(2)\).
reviewed by: Anatoli Kondrat'ev
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 5888497
zbMATH Keywords: finite simple groups
zbMATH Keywords: almost simple groups
zbMATH Keywords: groups of parabolic characteristic \(p\)
zbMATH Keywords: \(p\)-local subgroups
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.09.006
OpenAlex ID: W2003449419
cites work: The classification of the finite simple groups
cites work: Involutions in Chevalley groups over fields of even order
cites work: Q3684278
cites work: 2-fusion in finite groups
cites work: Q4857335
cites work: Transitive Permutation Groups in Which an Involution Central in a Sylow 2-Subgroup Fixes a Unique Point
cites work: The theory of finite groups. An introduction.
cites work: Q4426043
cites work: A 3-local characterization of \(U_6(2)\) and \(Fi_{22}\).
cites work: A characterization of the simple groups PSp(4,3) and PSp(6,2)
cites work: Finite groups with a certain centralizer of an element of order 3
cites work: Tits geometries and parabolic systems in finitely generated groups. I
cites work: Q3961400
cites work: An odd characterization of some simple groups
DOI: 10.1016/J.JALGEBRA.2010.09.006
description: scientific article; zbMATH DE number 5888497