An Investigation Into the Cyclically Presented Groups with Length Three Positive Relators

Abstract

We continue research into the cyclically presented groups with length three positive relators. We study small cancelation conditions, SQ-universality, and hyperbolicity, we obtain the Betti numbers of the groups’ abelianisations, we calculate the orders of the abelianisations of some groups, and we study isomorphism classes of the groups. Through computational experiments we assess how effective the abelianisation is as an invariant for distinguishing non-isomorphic groups.

Keywords:

• cyclically presented group
• isomorphism
• small cancelation
• hyperbolic group
• abelianisation

MATHEMATICS SUBJECT CLASSIFICATION:

• 20F05
• 20F06

Acknowledgments

We thank the referees of an earlier version of this paper for the helpful suggestions.

Additional information

Funding

Esamaldeen Mohamed acknowledges financial support of the Libyan Government.