Generalized small cancellation presentations for automatic groups.

DOI10.1515/GCC-2014-0007zbMATH Open1312.20032arXiv1406.7414OpenAlexW2963053505MaRDI QIDQ472157

Robert H. Gilman

Publication date: 18 November 2014

Published in: Groups - Complexity - Cryptology (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1406.7414

zbMATH Keywords

automatic groupssmall cancellation conditionspregroupsbiautomatic groupssmall cancellation presentations

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Groups acting on trees (20E08) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items (3)

EXTENSION OF GROUP PRESENTATIONS AND RELATIVE SMALL CANCELLATION THEORY I ⋮ Automatic Presentations for Cancellative Semigroups ⋮ Small cancellation theory and automatic groups. II

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