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The \(F^{a,b,c}\) conjecture is true. II. (English) Zbl 1178.20029

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.

MSC:

20F05 Generators, relations, and presentations of groups
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)

Software:

GAP
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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
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[7] The GAP Group, GAP—Groups, Algorithms, and Programming, Version 4.4, 2004
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[9] Havas, G.; Robertson, E. F., The \(F^{a, b, c}\) conjecture, I, Irish Math. Soc. Bull., 56, 75-80 (2005) · Zbl 1178.20028
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