Groups, Geometry, and Dynamics

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Volume 4, Issue 4, 2010, pp. 759–775
DOI: 10.4171/GGD/104

Published online: 2010-10-15

The cyclically presented groups with relators xixi+kxi+l

Martin Edjvet[1] and Gerald Williams[2]

(1) University of Nottingham, UK
(2) Essex University, Colchester, UK

Continuing Cavicchioli, Repovš, and Spaggiari’s investigations into the cyclic presentations < x1, … , xn | xixi+kxi+l = 1 (1 ≤ in) > we determine when they are aspherical and when they define finite groups; in these cases we describe the groups’ structures. In many cases we show that if the group is infinite then it contains a non-abelian free subgroup.

Keywords: Cyclically presented group, asphericity

Edjvet Martin, Williams Gerald: The cyclically presented groups with relators xixi+kxi+l. Groups Geom. Dyn. 4 (2010), 759-775. doi: 10.4171/GGD/104