ALGEBRA AND COMBINATORICS SEMINAR Tuesday 22 April 2008, 3pm in Room 67-641 George Havas, UQ Behind and beyond a theorem on groups related to trivalent graphs Abstract In 2006 we completed the proof of a five-part conjecture which 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. I explain how we derived the general proofs from specific cases. The conjecture essentially addressed only the finite groups in the family. 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. All welcome. ----------------------------------------------------------- http://www.maths.uq.edu.au/cdmc/Seminars.html