ABSTRACT

An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general theory o

chapter |3 pages

Introduction

chapter |1 pages

Acknowledgements

chapter 1|22 pages

Notation and Background

chapter 2|36 pages

Basics and Completely Decomposable Groups

chapter 3|10 pages

Cyclic Essential Extensions

chapter 4|30 pages

Regulating Subgroups and Regulators

chapter 5|6 pages

Local-global Relationships

chapter 6|32 pages

Groups with Cyclic Regulating Quotient

chapter 7|14 pages

Completely Decomposable Summands

chapter 8|16 pages

Anti—Representations

chapter 9|14 pages

Near-Isomorphism and Type-Isomorphism

chapter 10|14 pages

Fundamental Decomposition Theorems

chapter 11|50 pages

Finite Essential Extensions

chapter 12|32 pages

Classification

chapter 14|10 pages

In Search for Good Categories

chapter 15|20 pages

Associated Structures

chapter 16|20 pages

Literature