The cyclically presented groups with relators <var>x</var>_<var>i</var> <var>x</var>_{<var>i</var>+<var>k</var>} <var>x</var>_{<var>i</var>+<var>l</var>}

Abstract

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.