Ordered Permutation Groups

Ordered Permutation Groups

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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. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.show more

Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 1139241745
  • 9781139241748

Table of contents

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.show more