A computer algebra solution to a problem in finite groups. (Q1884040)
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scientific article; zbMATH DE number 2109603
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A computer algebra solution to a problem in finite groups. |
scientific article; zbMATH DE number 2109603 |
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A computer algebra solution to a problem in finite groups. (English)
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25 October 2004
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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)].
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finite varieties
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soluble groups
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laws
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identities
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Hasse-Weil bounds
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Gröbner bases
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algebraic varieties
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rational points
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