Rewriting systems, plain groups, and geodetic graphs

2020/09/07 by Elder, Murray, Piggott, Adam · 1 citation
#05C90 #20E06 #20F65 #68Q42 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2009.02885

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.

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