Generalized Small Cancellation Presentations for Automatic Groups

TL;DR

This paper extends small cancellation theory to a broader class of groups, demonstrating that certain generalized conditions ensure biautomaticity, thus expanding the known classes of automatic groups.

Contribution

It introduces a generalized small cancellation condition, extending the C(3)-T(6) condition, that guarantees biautomaticity for a wider range of groups.

Findings

Generalized small cancellation conditions imply biautomaticity.

All pieces having length one is a key assumption.

The new conditions encompass more groups than classical small cancellation.

Abstract

By a result of Gersten and Short finite presentations satisfying the usual non-metric small cancellation conditions present biautomatic groups. We show that in the case in which all pieces have length one, a generalization of the C(3)-T(6) condition yields a larger collection of biautomatic groups.