A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical considerations. It provides a self-contained account of certain natural generalizations of discrete groups.
"This is a timely and well-written book that brings together many theorems from an active area of combinatorial group theory. It will serve as both an excellent reference for researchers and a highly recommended text for graduate students."
---Bulletin of the London Mathematical Society
"…presents an introduction to combinatorial group theory through the study of one-relator groups and their generalisations…. The book is a useful addition to the literature on combinatorial group theory, and provides an accessible route into the subject for the beginner."
---Mathematical Reviews, 2000
"…the strength of the book is not a systematic introduction to some parts of combinatorial theory, but the wealth of information, the impressive number of results cited and reported on….serve[s] as a source of information and guide to the parts of combinatorial group theory centering around various tractable classes of generalization of one-relator and Fuchsian groups for which some kind of Freiheitssatz can be proved or some cancellation, diagrammatic or representation methods work, and also to learn some basic methods of combinatorial group theory as applied to the proposed classes of groups….interesting and challenging."
---Zentralblatt fur Mathematik, 2000
Introduction and historical remarks; preliminaries from combinatorial group theory; one-relator groups; discrete groups; one-relator products; one-relator products of cyclics; linear properties of one-relator products of cyclics; groups of F-type; related generalizations of discrete groups.