I will describe a new proof, joint with Adam Piggott (UQ), that groups presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length 3 are exactly the plain groups (free products of finite and infinite cyclic groups). Our proof relies on a new result about properties of embedded circuits in geodetic graphs, which may be of independent interest in graph theory.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
