The cyclically presented groups with relators $x_i{x}_{i+k}{x}_{i+l}$

Abstract

Continuing Cavicchioli, Repovš, and Spaggiari’s investigations into the cyclic presentations <$x_1,\dots ,x_n$ | $x_i{x}_{i+k}{x}_{i+l}$ = 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.