Ordered permutation groups
著者
書誌事項
Ordered permutation groups
（London Mathematical Society lecture note series, 55）
Cambridge University Press, 1981
大学図書館所蔵 件 / 全58件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Bibliography: p. 253-266
Includes indexes
内容説明・目次
内容説明
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.
目次
- 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.
「Nielsen BookData」 より
