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Finite complete rewriting systems for the Jantzen monoid and the Greendlinger group. (English) Zbl 0555.20036
Author’s abstract: ”It is shown that for the presentation (a,b; \(abbaab=\lambda)\) of the Jantzen monoid J no finite complete rewriting system exists that is based on a Knuth-Bendix ordering. However, a finite complete rewriting system is given for a different presentation of J that has four generators. Further, a finite complete rewriting system is given for the presentation (a,b,c; \(abc=cba)\) of the Greendlinger group G. This system induces a polynomial-time algorithm for the word problem for G.”
Reviewer: B.Pondelíček

20M05 Free semigroups, generators and relations, word problems
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F05 Generators, relations, and presentations of groups
Full Text: DOI
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