Algebraic Generalizations of Discrete Groups: A Path to Combinatorial Group Theory Through One-Relator Products (Chapman & Hall/CRC Pure and Applied Mathematics)

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. "Building on the achievements of combinatorial group theory, first established as a response to infinite discrete groups used in topological studies by Poincare, this reference/text thoroughly surveys one-relator groups and one-relator products of cyclic groups - extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical constructions."--BOOK JACKET. "Algebraic Generalizations of Discrete Groups is an indispensable reference for pure and applied mathematicians, algebraist, and number theorists, and a superb text for graduate students in these disciplines."--BOOK JACKET. A one-relator group or a group with a single defining relation is a group which has a presentation of the form < x1, ..., xn; R >. Benjamin Fine, Gerhard Rosenberger. Includes Bibliographical References (p. 291-308) And Indexes.