Generalized Small Cancellation Presentations for Automatic Groups
Robert H. Gilman

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.
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