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Continuing Cavicchioli, Repovš, and Spaggiari's investigations into the cyclic presentations 〈x 1 ,...,x n | x i x i+k x i+l D 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. © European Mathematical Society

The cyclically presented groups with relators $x_ix_{i+k}x_{i+l}$