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  3. Ordered Permutation Groups
  • Cited by 7
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2010
      January 1982
      ISBN:
      9780511721243
      9780521241908
      DOI:
      https://doi.org/10.1017/CBO9780511721243
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.499kg, 332 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      London Mathematical Society Lecture Note Series (55)
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    London Mathematical Society Lecture Note Series (55)
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    Book description

    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.

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