Abstract

Publisher Summary The purpose of the Knuth–Bendix completion procedure for a system of reductions R is to produce a system that is equationally equivalent to R and reduces each word to a unique normal form. The procedure very often does not terminate and results in an infinite limit system R ∞ . If R ∞ can be “nicely” described in a finitary way then it very often is as useful as a finite complete system. This chapter discusses in the case of groups the information provided by a regular limit system, and also explains cases in which the limit system is not even regular. Moreover, both questions are connected with properties of the growth function of the group.

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