A characterization of \(SL_ 2(k)\) by its quadratic action on the natural module
type: Item
instance of: scholarly article
title: A characterization of \(SL_ 2(k)\) by its quadratic action on the natural module
zbMATH Open document ID: 0810.20037
DOI: 10.1007/BF01207539
author: Hans Cuypers
published in: Archiv der Mathematik
publication date: 1995-04-17T00:00:00Z
review text: The author characterizes the group \(SL_ 2(k)\) by properties of its quadratic action on the natural module, where \(k\) is a skew field or a Cayley division algebra, compare \textit{F. Timmesfeld} [Forum Math. 6, No. 2, 209-231 (1994; Zbl 0802.51003)]. The assumptions on the action concern mainly a system of abelian subgroups, which turn out to be transvection subgroups. The proof uses geometric methods developed by the author and by \textit{J. I. Hall} [Proc. Lond. Math. Soc., III. Ser. 58, No. 1, 89-111 (1989; Zbl 0673.20015)] for the study of groups generated by \(k\)- transvection groups.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 493380
zbMATH Keywords: quadratic action
zbMATH Keywords: skew field
zbMATH Keywords: Cayley division algebra
zbMATH Keywords: transvection subgroups
zbMATH Keywords: groups generated by \(k\)-transvection groups
reviewed by: Theo Grundhöfer
MaRDI profile type: Publication
cites work: Symplectic geometries, transvection groups, and modules
cites work: Graphs, Geometry, 3-Transpositions, and Symplectic F 2 -Transvection Groups
cites work: A characterization of \(\text{SL}(2,p^n)\), \(p\geq 5\).
cites work: Q5683869
cites work: On quadratic GF(2)-modules for Chevalley groups over fields of odd order
cites work: Quadratic action and the natural module for \(SL_ 2(k)\)
cites work: Q5645602
cites work: Groups generated by k-transvections
full work available at URL: https://doi.org/10.1007/bf01207539
OpenAlex ID: W2160393407
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description: scientific article; zbMATH DE number 493380