A remark about combings of groups
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Int. J. of Algebra and Computation, vol 3, 1993, 575-581 (with Martin
Bridson).
     
A combing is simply a choice of normal form for group elements relative
to a fixed finite set of generators, but typically the set of words in
normal form is required to satisfy language theoretic constraints when
viewed as a formal language over the alphabet of generators, and
geometric constraints when interpreted as a collection of paths in the
Cayley graph of the group.  Language theoretic and geometric conditions
afford new ways of looking at finitely generated groups, and it is of
interest to consider how various classes of groups may be characterized
in terms of the combings which they admit.
 
We give a simple example of a class of groups defined in terms of the
combings which they admit with respect to an arbitrary set of generators,
and show that it is not necessary to include the language theoretic
constraint as part of the definition.