Thomas, Richard M. Group presentations where the relators are proper powers. (English) Zbl 0855.20033 Campbell, C. M. (ed.) et al., Groups ’93 Galway/St. Andrews’. Proceedings of the international conference, Galway, Ireland, August 1-14, 1993. Volume 2. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 212, 549-560 (1995). This excellent survey article concerns group presentations where the relators are proper powers. The most known groups with such a presentation are the so called generalized triangle groups \(\langle a,b; a^m=b^n=R^k(a,b)=1\rangle\) where \(m,n,k\geq 2\) and \(R(a,b)\) is a cyclically reduced word involving both \(a\) and \(b\). The main question of interest here is that of asking when such a group presentation with all relators proper powers is finite or infinite.For the entire collection see [Zbl 0839.00022]. Reviewer: G.Rosenberger (Dortmund) Cited in 6 Documents MSC: 20F05 Generators, relations, and presentations of groups Keywords:presentations; relators; proper powers; generalized triangle groups; cyclically reduced words PDFBibTeX XMLCite \textit{R. M. Thomas}, Lond. Math. Soc. Lect. Note Ser. 212, 549--560 (1995; Zbl 0855.20033)