Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 24, pages 493-509.

Hairdressing in groups: a survey of combings and formal languages

Sarah Rees

Abstract. A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This article surveys results for combable groups, in particular in the case where the combing is a formal language.

Keywords. Combings, formal languages, fellow travellers, automatic groups

AMS subject classification. Primary: 20F10, 20-04, 68Q40. Secondary: 03D40.

E-print: arXiv:math.GR/9810201

Submitted: 15 November 1997. Published: 29 October 1998.

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Sarah Rees
University of Newcastle, Newcastle NE1 7RU, UK
Email: Sarah.Rees@ncl.ac.uk

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