Havas, George; Robertson, Edmund F.; Sutherland, Dale C. The \(F^{a,b,c}\) conjecture is true. II. (English) Zbl 1178.20029 J. Algebra 300, No. 1, 57-72 (2006). Summary: In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. Cited in 1 ReviewCited in 3 Documents MSC: 20F05 Generators, relations, and presentations of groups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:presentations; finite groups; computation; coset enumerators; trivalent graphs Citations:Zbl 0381.20025; Zbl 0466.20013; Zbl 0494.20016; Zbl 1178.20028 Software:GAP PDFBibTeX XMLCite \textit{G. Havas} et al., J. Algebra 300, No. 1, 57--72 (2006; Zbl 1178.20029) Full Text: DOI References: [1] Campbell, C. M.; Coxeter, H. S.M.; Robertson, E. F., Some families of finite groups having two generators and two relations, Proc. R. Soc. Lond. Ser. A, 357, 423-438 (1977) · Zbl 0381.20025 [2] Campbell, C. M.; Robertson, E. F., On 2-generator 2-relation soluble groups, Proc. Edinburgh Math. Soc. (2), 23, 269-273 (1980) · Zbl 0466.20013 [3] Campbell, C. M.; Robertson, E. F., Groups related to \(F^{a, b, c}\) involving Fibonacci numbers, (The Geometric Vein (1981), Springer-Verlag: Springer-Verlag New York), 569-576 · Zbl 0494.20016 [4] Campbell, C. M.; Robertson, E. F., On the \(F^{a, b, c}\) conjecture, Mitt. Math. Sem. Giessen, 164, 25-36 (1984) · Zbl 0571.20026 [5] Coxeter, H. S.M.; Frucht, R.; Powers, D. L., Zero-Symmetric Graphs. Trivalent Graphical Regular Representations of Groups (1981), Academic Press: Academic Press New York · Zbl 0548.05031 [6] Foster, R. M., The Foster Census (1988), Charles Babbage Research Centre: Charles Babbage Research Centre Winnipeg, MB [7] The GAP Group, GAP—Groups, Algorithms, and Programming, Version 4.4, 2004 [8] G. Havas, C. Ramsay, On proofs in finitely presented groups, in: Groups St. Andrews, 2005, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, in press; G. Havas, C. Ramsay, On proofs in finitely presented groups, in: Groups St. Andrews, 2005, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, in press · Zbl 1120.20032 [9] Havas, G.; Robertson, E. F., The \(F^{a, b, c}\) conjecture, I, Irish Math. Soc. Bull., 56, 75-80 (2005) · Zbl 1178.20028 [10] G. Havas, E.F. Robertson, D.C. Sutherland, Behind and beyond the proof of the \(F^{a , b , c}\); G. Havas, E.F. Robertson, D.C. Sutherland, Behind and beyond the proof of the \(F^{a , b , c}\) · Zbl 1178.20029 [11] Perkel, M., Groups of type \(F^{a, b, - c}\), Israel J. Math., 52, 167-176 (1985) · Zbl 0581.20033 [12] Spaggiari, F., On certain classes of finite groups, Ricerche Mat., 46, 31-43 (1997) · Zbl 0949.20023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.