UID:
almafu_9959239118702883
Format:
1 online resource (xlix, 266 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88384-4
,
1-107-36588-0
,
1-107-37061-2
,
1-107-36097-8
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1-107-37027-2
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1-299-40369-7
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1-107-36342-X
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0-511-72124-2
Series Statement:
London Mathematical Society lecture note series ; 55
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Title; Copyright; Dedication; Contents; PREFACE; BACKGROUND TERMS AND NOTATION; EXPLANATION OF DIAGRAMS.; PART I OPENING THE INNINGS; CHAPTER 1 INTRODUCTION; 1.1. A(Ω).; 1.2 ACTIONS OF GROUPS OT CHAINS.; 1.3. PARTIALLY ORDERED GROUPS.; 1.4. CONGRUENCES.; 1.5. STABILISERS AND BLOCKS.; 1.6. TRANSITIVE ACTIONS.; 1. 7. PRIMITIVE COMPONENTS.; 1.8. DEDEKIND COMPLETION AND CHARACTER.; 1.9. BUMPS AND SUPPORTS.; 1.10. MULTIPLE TRANSITIVITY.; 1.11. IDENTITIES.; CHAPTER 2 DOUBLY TRANSITIVE A(Ω); 2.1. GEOMETRY VERSUS ALGEBRA.; 2.2. DIVISIBILITY AND CONJUGACY IN A (Ω)
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2.3. THE NORMAL SUBGROUPS OF A (Ω)2.4. THE AUTOMORPHISMS OF A(Ω); 2.5. EMBEDDING IN DOUBLY TRANSITIVE A(Ω); PART II THE STRUCTURE THEORY; CHAPTER 3 CONGRUENCES AND BLOCKS; 3.1. TRANSITIVE ORDERED PERMUTATION GROUPS.; 3.2. INTRANSITIVE ORDERED PERMUTATION GROUPS.; CHAPTER 4 PRIMITIVE ORDERED PERMUTATION GROUPS; 4.1. TRANSITIVE PRIMITIVE ORDERED PERMUTATION GROUPS.; 4.2. TOTALLY ORDERED TRANSITIVE ORDERED PERMUTATION GROUPS.; 4.3. PERIODIC PRIMITIVE l-PERMUTATION GROUPS.; 4.4. INTRANSITIVE PRIMITIVE ORDERED PERMUTATION GROUPS.; 4.5. THE PROOF OF_ THEOREM 4D.; CHAPTER 5 THE WREATH PRODUCT
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PART III APPLICATIONS TO ORDERED PERMUTATION GROUPS; CHAPTER 6 SIMPLE l-PERMUTATION GROUPS; CHAPTER 7 UNIQUENESS OF REPRESENTATION; 7.1. l-PERMUTATION GROUPS.; 7.2. ORDERED PERMUTATION GROUPS.; CHAPTER 8 POINTWISE SUPREMA AND CLOSED SUBGROUPS; 8.1.CLOSED STABILISER SUBGROUPS.; 8.2. POINTWISE SUPREMA.; 8.3. CLOSED SUBGROUPS OF l-GROUPS.; CHAPTER 9 AUTOMORPHISMS OF A(Ω); PART IV APPLICATIONS TO LATTICE-ORDERED GROUPS; CHAPTER 10 EMBEDDING THEOREMS FOR LATTICE-ORDERED GROUPS; CHAPTER 11 NORMAL VALUED LATTICE-ORDERED GROUPS; PART V THE AUTHOR'S PREROGATIVE
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CHAPTER 12 ALGEBRAICALLY CLOSED LATTICE-ORDERED GROUPS; CHAPTER 13 THE WORD PROBLEM FOR LATTICE-ORDERED GROUPS; APPENDIX I; APPENDIX II; SOME UNSOLVED PROBLEMS; TEE ABELIAN GROUPABILITY PROBLEM.; ORDERABILITY PROBLEMS.; MULTIPLE TRANSITIVITY PROBLEMS.; TEE PRIMITIVITY PROBLEM.; PROBLEMS ON_ SIMPLICITY AND ^SIMPLICITY.; EXISTENTIALLY CLOSED Z-PERMUTATION GR; THE LATERAL COMPLETION PROBLEM.; WORD PROBLEM TYPE PROBLEMS.; BIBLIOGRAPHY; ANNOTATIONS; INDEX; INDEX OF SYMBOLS
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English
Additional Edition:
ISBN 0-521-24190-1
Language:
English
URL:
https://doi.org/10.1017/CBO9780511721243
