English

Rewriting systems, plain groups, and geodetic graphs

Group Theory 2021-12-16 v2

Abstract

We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length 3 if and only if the group is plain. Our proof goes via a new result concerning properties of embedded circuits in geodetic graphs, which may be of independent interest in graph theory.

Keywords

Cite

@article{arxiv.2009.02885,
  title  = {Rewriting systems, plain groups, and geodetic graphs},
  author = {Murray Elder and Adam Piggott},
  journal= {arXiv preprint arXiv:2009.02885},
  year   = {2021}
}

Comments

11 pages, 10 figures, minor edits and corrections

R2 v1 2026-06-23T18:21:05.611Z