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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].

##### MSC:
 20F05 Generators, relations, and presentations of groups