Abstract
In this paper we apply rewriting techniques to certain types of string-rewriting systems related to power-commutation-presentations for finitely generated (f.g.) abelian groups, f.g. nilpotent groups, f.g. supersolvable groups and f.g. polycyclic groups. We develop a modified version of the Knuth-Bendix completion procedure which transforms such a string-rewriting system into an equivalent canonical system of the same type. This completion procedure terminates on all admissible inputs and works with a fixed reduction ordering on strings. Since canonical string-rewriting systems have decidable word problem this procedure shows that the systems above have uniformly decidable word problem. In addition, this result yields a new purely combinatorial proof for the well-known uniform decidability of the word problem for the corresponding groups.
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© 1989 Springer-Verlag Berlin Heidelberg
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Wissmann, D. (1989). Applying rewriting techniques to groups with power-commutation-presentations. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_36
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DOI: https://doi.org/10.1007/3-540-51084-2_36
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