ABSTRACT

This study in combinatorial group theory introduces the concept of automatic groups. It contains a succinct introduction to the theory of regular languages, a discussion of related topics in combinatorial group theory, and the connections between automatic groups and geometry which motivated the development of this new theory. It is of interest to

part I|2 pages

I An Introduction to Automatic Groups

chapter 2|36 pages

Automatic Groups

chapter 4|14 pages

Abelian and Euclidean Groups

chapter 5|12 pages

Finding the Automatic Structure: Theory

chapter 7|26 pages

Asynchronous Automatic Groups

chapter 8|18 pages

Nilpotent Groups

part II|2 pages

Topics in the Theory of Automatic Groups

chapter 9|30 pages

Braid Groups

chapter 11|30 pages

Geometrically Finite Groups

chapter 12|42 pages

Three-Dimensional Manifolds