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Complete presentations of Coxeter groups. (English) Zbl 1041.20027
A complete presentation of a group or monoid \(M\) is a presentation of \(M\) that is complete when regarded as a string rewriting system. It allows to write any word on the generators in a canonical form.
The authors give a complete presentation for irreducible finite Coxeter groups of type \(D_n\). The proof is by induction on \(n\). The complete presentation of \(D_4\) was obtained using GAP-3.
MSC:
20F55 Reflection and Coxeter groups (group-theoretic aspects)
68Q42 Grammars and rewriting systems
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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