On the geometry of normal forms in discrete groups

We study normal forms irT finitely generated groups from the geometric viewpoint of combings. We introduce notions of combability considerably weaker than those commonly in use. We prove that groups which satisfy these conditions are finitely presented and satisfy isoperimetric and isodiametric The word problem for finitely generated groups was first formulated by Dehn in his famous article of 1910 [11]..Subsequently, Dehn demonstrated the intimate connection between the word problem and the geometry of paths in the Cayley graph of the group (see [12]). In a somewhat different guise, this idea played