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dc.contributor.authorHavas, George
dc.contributor.authorRobertson, Edmund F.
dc.contributor.authorSutherland, Dale C.
dc.date.accessioned2012-03-26T23:52:47Z
dc.date.available2012-03-26T23:52:47Z
dc.date.issued2008-12
dc.identifier.citationHavas , G , Robertson , E F & Sutherland , D C 2008 , ' Behind and beyond a theorem on groups related to trivalent graphs ' , Journal of the Australian Mathematical Society , vol. 85 , no. 3 , pp. 323-332 . https://doi.org/10.1017/S1446788708000852en
dc.identifier.issn1446-7887
dc.identifier.otherPURE: 18141015
dc.identifier.otherPURE UUID: bf312c71-933c-4b1c-81ea-20f8be9babf7
dc.identifier.otherWOS: 000264125400003
dc.identifier.otherScopus: 67650308194
dc.identifier.urihttps://hdl.handle.net/10023/2462
dc.description.abstractIn 2006 we completed the proof of a five-part conjecture that was made in 1977 about a family of groups related to trivalent graphs. This family covers all 2-generator, 2-relator groups where one relator specifies that a generator is an involution and the other relator has three syllables. Our proof relies upon detailed but general computations in the groups under question. The proof is theoretical, but based upon explicit proofs produced by machine for individual cases. Here we explain how we derived the general proofs from specific cases. The conjecture essentially addressed only the finite groups in the family. Here we extend the results to infinite groups, effectively determining when members of this family of finitely presented groups are simply isomorphic to a specific quotient.
dc.format.extent10
dc.language.isoeng
dc.relation.ispartofJournal of the Australian Mathematical Societyen
dc.rightsCopyright © Australian Mathematical Society 2009en
dc.subjectFinitely presented groupsen
dc.subjectProofsen
dc.subjectTodd-Coxeter coset enumerationen
dc.subjectTrivalent graphsen
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleBehind and beyond a theorem on groups related to trivalent graphsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1017/S1446788708000852
dc.description.statusPeer revieweden
dc.identifier.grantnumberEP/C523229/1en


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