On a small cancellation theorem of Gromov

TL;DR

This paper provides a combinatorial proof of Gromov's theorem, expanding small cancellation theory to include group presentations derived from labelled graphs, thereby broadening its applicability.

Contribution

It offers a new combinatorial proof of Gromov's small cancellation theorem for graph-labelled group presentations, extending the theory's scope.

Findings

Extended small cancellation theory to graph-labelled group presentations

Provided a combinatorial proof of Gromov's theorem

Broadened applicability of small cancellation conditions

Abstract

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.