Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 11, pages 249-260.

Automatic groups, subgroups and cosets

Derek F Holt

Abstract. The history, definition and principal properties of automatic groups and their generalisations to subgroups and cosets are reviewed briefly, mainly from a computational perspective. A result about the asynchronous automaticity of an HNN extension is then proved and applied to an example that was proposed by Mark Sapir.

Keywords. Automatic Groups, HNN extensions

AMS subject classification. Primary: 20F32. Secondary: 20F05.

E-print: arXiv:math.GR/9810190

Submitted: 26 August 1997. Published: 26 October 1998.

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Derek F Holt
Mathematics Institute, University of Warwick
Coventry, CV4 7AL, UK.
Email: dfh@maths.warwick.ac.uk

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