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Title: Behind and beyond a theorem on groups related to trivalent graphs
Authors: Havas, George
Robertson, Edmund F.
Sutherland, Dale C.
Keywords: Finitely presented groups
Todd-Coxeter coset enumeration
Trivalent graphs
QA Mathematics
Issue Date: Dec-2008
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 . , 10.1017/S1446788708000852
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.
Version: Publisher PDF
Status: Peer reviewed
ISSN: 1446-7887
Type: Journal article
Rights: Copyright © Australian Mathematical Society 2009
Appears in Collections:Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
University of St Andrews Research
Applied Mathematics Research

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