JournalsggdVol. 4 , No. 4pp. 759–775

The cyclically presented groups with relators <var>x</var><sub><var>i</var></sub> <var>x</var><sub><var>i</var>+<var>k</var></sub> <var>x</var><sub><var>i</var>+<var>l</var></sub>

  • Martin Edjvet

    University of Nottingham, UK
  • Gerald Williams

    Essex University, Colchester, UK
The cyclically presented groups with relators <var>x</var><sub><var>i</var></sub> <var>x</var><sub><var>i</var>+<var>k</var></sub> <var>x</var><sub><var>i</var>+<var>l</var></sub> cover
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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.

Cite this article

Martin Edjvet, Gerald Williams, The cyclically presented groups with relators <var>x</var><sub><var>i</var></sub> <var>x</var><sub><var>i</var>+<var>k</var></sub> <var>x</var><sub><var>i</var>+<var>l</var></sub>. Groups Geom. Dyn. 4 (2010), no. 4 pp. 759–775

DOI 10.4171/GGD/104