Proving a group infinite (Q1113281)

A method for proving groups infinite is described. It is based on a version of the Golod-Shafarevich theorem proved by \textit{W. Gaschütz} and \textit{M. F. Newman} [J. Reine Angew. Math. 245, 172-176 (1970; Zbl 0221.20023)]. The method is used to show that ``the last of the Fibonacci groups'' is infinite: this group is generated by \(\{a_ 1,...,a_ 9\}\) subject to defining relations \(a_ 1a_ 2=a_ 3,...,a_ 9a_ 1=a_ 2\); see a paper by \textit{G. Havas}, \textit{J. S. Richardson}, \textit{L. S. Sterling} [Proc. R. Soc. Edinb., Sect. A 83, 199-203 (1979; Zbl 0416.20026)] for an earlier discussion of this group. The information needed to apply the criterion for infiniteness was extracted from the presentation with the aid of a computer using the system SPAS created at Lehrstuhl D für Mathematik in Aachen.