Table of Contents

Introduction v

Part I: Stallings's theorem about pregroups;

introduction to pregroups of finite height

1. The definition of a pregroup 1

2. The pregroups of finite height 5

3. The subpregroup of units 13

Part II: A presentation for the universal group

of a pregroup of finite height.

4. Pregroup actions and generating sets 20

5. A presentation for the universal group of a

pregroup of finite height 29

Part III: The relationship between pregroups

and graphs of groups

6. A graph of groups structure for pregroups

of finite height 39

7. A pregroup structure for graphs

of groups of finite diameter 55

References 73

in