The Theory of Lattice-Ordered Groups

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This volume makes both classical and new results of the theory of lattice-ordered groups available to a wide range of mathematicians in a comprehensive way, explaining the structure of the theory as well as indicating its applications. The book contains the foundations of the theory of lattice-ordered groups, and the theory of ordered permutation groups. It describes totally-ordered and right-ordered groups, and highlights the theory of varieties and quasi-varieties of lattice-ordered groups. The distinguishing feature of this work is the group-theoretical and universal algebra attitude to the theory of lattice-ordered groups. This volume will be of interest to graduate students and researchers with a basic knowledge of group theory. It serves as an excellent introduction to the theory of partially ordered groups, and as an overview of new ideas and results in this theory.