Groups, Geometry, and Dynamics
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Published online: 2010-10-15
The cyclically presented groups with relators xi xi+k xi+lMartin Edjvet and Gerald Williams (1) University of Nottingham, UK
(2) Essex University, Colchester, UK
Continuing Cavicchioli, Repovš, and Spaggiari’s investigations into the cyclic presentations < x1, … , xn | xi xi+k xi+l = 1 (1 ≤ i ≤ n) > 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 xi xi+k xi+l. Groups Geom. Dyn. 4 (2010), 759-775. doi: 10.4171/GGD/104