A computer algebra solution to a problem in finite groups.
type: Item
instance of: scholarly article
title: A computer algebra solution to a problem in finite groups.
zbMATH Open document ID: 1071.20025
DOI: 10.4171/RMI/355
author: Gert-Martin Greuel
published in: Revista Matemática Iberoamericana
publication date: 2004-10-25T00:00:00Z
full work available at URL: https://eudml.org/doc/39610
review text: The author reports on an attempt to describe a sequence \(U_1,U_2,\dots\) of words in two variables such that the finite group \(G\) is soluble iff the identity \(U_n=1\) holds in \(G\) for all but finitely many \(n\). The case of the Suzuki groups is left open. For a complete result see \textit{T. Bandman}, \textit{G.-M. Greuel}, \textit{F. Grunewald}, \textit{B. Kunyavskij}, \textit{G. Pfister} and \textit{E. Plotkin} [C. R., Math., Acad. Sci. Paris 337, No. 9, 581-586 (2003; Zbl 1047.20014)].
reviewed by: Rolf Brandl
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20-04
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20F12
zbMATH DE Number: 2109603
zbMATH Keywords: finite varieties
zbMATH Keywords: soluble groups
zbMATH Keywords: laws
zbMATH Keywords: identities
zbMATH Keywords: Hasse-Weil bounds
zbMATH Keywords: Gröbner bases
zbMATH Keywords: algebraic varieties
zbMATH Keywords: rational points
describes a project that uses: CoCoA
describes a project that uses: SINGULAR
describes a project that uses: Macaulay2
MaRDI profile type: Publication
cites work: Q4336964
cites work: Thompson's problem (\(\sigma^2=3\)) With two appendices. I: The numerical verification of Thompson's identity by Andrew Odlyzko: II: A check of the Ree group conjecture for small fields by David Hunt
cites work: Q2781760
cites work: Q4790431
cites work: SINGULAR
cites work: Geometrical equivalence of groups
cites work: Nonsolvable finite groups all of whose local subgroups are solvable
OpenAlex ID: W2007048379
description: scientific article; zbMATH DE number 2109603