TOWARDS QUANTITATIVECLASSIFICATION OF CAYLEYAUTOMATIC GROUPS

Abstract

In this paper we address the problem of quantitative classification of
Cayley automatic groups in terms of a certain numerical characteristic
which we earlier introduced for this class of groups. For this numerical
characteristic we formulate and prove a fellow traveler property, show
its relationship with the Dehn function and prove its invariance with
respect to taking finite extension, direct product and free product. We
study this characteristic for nilpotent groups with a particular accent on
the Heisenberg group, the fundamental groups of torus bundles over the
circle and groups of exponential growth