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A computer algebra solution to a problem in finite groups. (English) Zbl 1071.20025

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 T. Bandman, G.-M. Greuel, F. Grunewald, B. Kunyavskij, G. Pfister and E. Plotkin [C. R., Math., Acad. Sci. Paris 337, No. 9, 581-586 (2003; Zbl 1047.20014)].
Reviewer: Rolf Brandl (Hof)

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20-04 Software, source code, etc. for problems pertaining to group theory
14G05 Rational points
20E10 Quasivarieties and varieties of groups
20F12 Commutator calculus

Citations:

Zbl 1047.20014
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References:

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