Commentarii Mathematici Helvetici

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Volume 78, Issue 4, 2003, pp. 752–771
DOI: 10.1007/s00014-003-0776-7

Published online: 2003-12-31

Combings of groups and the grammar of reparameterization

Martin R. Bridson[1]

(1) University of Oxford, UK

A new construction of combings is used to distinguish between several previously indistinguishable classes of groups associated to the theory of automatic groups and non-positive curvature in group theory. We construct synchronously bounded combings for a class of groups that are neither bicombable nor automatic. The linguistic complexity of these combings is analysed: in many cases the language of words in the combing is an indexed language.

Keywords: Finitely presented groups, combings,a utomatic groups, indexed languages

Bridson Martin: Combings of groups and the grammar of reparameterization. Comment. Math. Helv. 78 (2003), 752-771. doi: 10.1007/s00014-003-0776-7