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Behind and beyond a theorem on groups related to trivalent graphs
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dc.contributor.author | Havas, George | |
dc.contributor.author | Robertson, Edmund F. | |
dc.contributor.author | Sutherland, Dale C. | |
dc.date.accessioned | 2012-03-26T23:52:47Z | |
dc.date.available | 2012-03-26T23:52:47Z | |
dc.date.issued | 2008-12 | |
dc.identifier.citation | Havas , 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/S1446788708000852 | en |
dc.identifier.issn | 1446-7887 | |
dc.identifier.other | PURE: 18141015 | |
dc.identifier.other | PURE UUID: bf312c71-933c-4b1c-81ea-20f8be9babf7 | |
dc.identifier.other | WOS: 000264125400003 | |
dc.identifier.other | Scopus: 67650308194 | |
dc.identifier.uri | https://hdl.handle.net/10023/2462 | |
dc.description.abstract | In 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.extent | 10 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the Australian Mathematical Society | en |
dc.rights | Copyright © Australian Mathematical Society 2009 | en |
dc.subject | Finitely presented groups | en |
dc.subject | Proofs | en |
dc.subject | Todd-Coxeter coset enumeration | en |
dc.subject | Trivalent graphs | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Behind and beyond a theorem on groups related to trivalent graphs | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1017/S1446788708000852 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | EP/C523229/1 | en |
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