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Computation of nilpotent engel groups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Werner Nickel
Werner Nickel
Affiliation:
Fachbereich Mathematik AG 2 TU Darmstadt Schloßgartenstraße 7 D-64289 Darmstadt Germany URL: www.mathematik.tu-darmstadt.de/nickel e-mail: [email protected]
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Abstract

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This paper reports on a facility of the ANU NQ program for computation of nilpotent groups that satisfy an Engel-n identity. The relevant details of the algorithm are presented together with results on Engel-n groups for moderate values of n.

Keywords

Engel groupsnilpotent quotient algorithmHigman's Lemma.

MSC classification

Secondary: 20F05: Generators, relations, and presentations 20F45: Engel conditions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 2 , October 1999 , pp. 214 - 222
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]The GAP Group, Aachen, St Andrews, ‘GAP – Groups, Algorithms, and Programming, Version 4’, 1998 (http://www-gap.dcs.st-and.ac.uk/~gap).Google Scholar
[2]Havas, G. and Newman, M. F., ‘Application of computers to questions like those of Burnside’, in: Burnside groups (Bielefeld, 1977), Lecture Notes in Math. 806 (Springer, Berlin, 1980) pp. 211–230.CrossRefGoogle Scholar
[3]Higman, Graham, ‘Some remarks on varieties of groups’, Quart. J. Math. Oxford ser. (2) 10 (1959), 165–178.CrossRefGoogle Scholar
[4]Leedham-Green, C. R. and Soicher, L. H., ‘Symbolic collection using Deep Thought’, LMS. J. Comput. Math. 1 (1998), 9–24.CrossRefGoogle Scholar
[5]Merkeitz, W. W., Symbolische Multiplikation in nilpotenten Gruppen mit Deep Thought (Diplomarbeit, RWTH Aachen, 1997).Google Scholar
[6]Nickel, W., ‘Computing nilpotent quotients of finitely presented groups’, in: Geometric and computational perspective on infinte groups (eds. Baumslag, G. et al. ), Amer. Math. Soc. DIMACS Series Vol. 25 1994 (DIMACS, New Brunswick, 1995) pp. 175–191.CrossRefGoogle Scholar
[7]Robinson, D. J., A course in the theory of groups, Graduate Texts in Math. 80 (Springer, New York, 1982).CrossRefGoogle Scholar
[8]Sims, C. C., Computation with finitely presented groups (Cambridge University Press, Cambridge, 1994).CrossRefGoogle Scholar
[9]Vaughan-Lee, M. R., ’An aspect of the nilpotent quotient algorithm’, in: Computational group theory (Academic Press, New York, 1984) pp. 76–83.Google Scholar
[10]Vaughan-Lee, M. R. ’Engel-4 groups of exponent 5’, Proc. London Math. Soc. 74 (1997), 306–334.CrossRefGoogle Scholar
[11]Zel'manov, E. I., ‘Solution of the restricted Burnside problem for groups of odd exponent’, Math. USSR-lzv. 36 (1991), 41–60CrossRefGoogle Scholar