Behind and beyond a theorem on groups related to trivalent graphs
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.
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
Publication
Journal of the Australian Mathematical Society
Status
Peer reviewed
ISSN
1446-7887Type
Journal article
Rights
Copyright © Australian Mathematical Society 2009
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.