Ordered Permutation Groups

Klappentext As a result of the work of the nineteenth-century mathematician Arthur Cayley! algebraists and geometers have extensively studied permutation of sets. Zusammenfassung As a result of the work of the nineteenth-century mathematician Arthur Cayley! algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered! there is a natural subgroup to study! namely the set of permutations that preserves that order. Inhaltsverzeichnis Part I. Opening the innings: 1. Introduction; 2. Doubly Transitive A; Part II. The structure theory: 3. Congruences and blocks; 4. Primitive ordered permutation groups; 5. The wreath product; Part III. Applications to ordered permutation groups: 6. Simple-permutation groups; 7. Uniqueness of representation; 8. Pointwise suprema and closed subgroups; Part IV. Applications to lattice-ordered groups: 10. Embedding theorums for lattice-ordered groups; 11. Normal valued lattice-ordered groups; Part V. The author's perogative: 12. Algebraically closed lattice-ordered groups; 13. The word problem for lattice-ordered groups.

Zusammenfassung
As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order.

Inhalt
Part I. Opening the innings: 1. Introduction; 2. Doubly Transitive A; Part II. The structure theory: 3. Congruences and blocks; 4. Primitive ordered permutation groups; 5. The wreath product; Part III. Applications to ordered permutation groups: 6. Simple-permutation groups; 7. Uniqueness of representation; 8. Pointwise suprema and closed subgroups; Part IV. Applications to lattice-ordered groups: 10. Embedding theorums for lattice-ordered groups; 11. Normal valued lattice-ordered groups; Part V. The author's perogative: 12. Algebraically closed lattice-ordered groups; 13. The word problem for lattice-ordered groups.

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