Complete Presentations of Direct Products of Groups

  • Complete presentations provide a natural solution to the word problem in monoids and groups. Here we give a simple way to construct complete presentations for the direct product of groups, when such presentations are available for the factors. Actually, the construction we are referring to is just the classical construction for direct products of groups, which has been known for a long time, but whose completeness-preserving properties had not been detected. Using this result and some known facts about Coxeter groups, we sketch an algorithm to obtain the complete presentation of any finite Coxeter group. A similar application to Abelian and Hamiltonian groups is mentioned.

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Author:Miguel Borges-Trenard, Hebert Perez-Roses
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7632
Serie (Series number):Reports on Computer Algebra (ZCA Report) (24)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):1999/11/11
Tag:Abelian groups; Coxeter groups; Hamiltonian groups; Word problem; complete presentations; direct product
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011