Right-ordered groups / Valerii M. Kopytov and Nikolai Ya. Medvedev.
Idioma: Inglés Lenguaje original: Ruso Series Sibirskaia shkola algebry i logiki: Editor: New York : Consultants Bureau, c1996Descripción: ix, 250 p. ; 24 cmISBN: 0306110601Otra clasificación: 06F15 (20F60)Chapter 1. Introduction [1] 1.1. Partially Ordered Sets [1] 1.2. Lattices [4] 1.3. Properties of Lattices [7] 1.4. Orders on Groups [12] 1.5. Positive Cones [15] 1.6. Basic Notions [19] Chapter 2. Systems of Convex Subgroups [29] 2.1. General Properties [29] 2.2. Archimedean Groups [33] 2.3. Totally Ordered Groups [35] 2.4. Conradian Groups [37] Chapter 3. Orderability Conditions [45] 3.1. Semigroup Conditions [45] 3.2. Sufficient Conditions [49] 3.3. Group Conditions for Total Orderability [52] 3.4. Groups of Automorphisms [57] 3.5. Connection with Totally Ordered Groups [59] 3.6. Fully Orderable Groups [62] Chapter 4. Groups of Order Automorphisms [73] 4.1. Preliminaries [73] 4.2. Wreath Products [85] 4.3. Order Types of Right-Ordered Groups [97] 4.4. The Chehata Groups and the Dlab Groups [100] 4.5. Embeddings [113] Chapter 5. Relatively Convex Subgroups [121] 5.1. Orderable Representations [121] 5.2. A Finite Number of Right Orders [132] 5.3. A Finite Number of Total Orders [142] 5.4. Center of Right-Ordered Groups [148] 5.5. Criteria for Orderability [153] 5.6. Centers of “Small” Subgroups [157] Chapter 6. Orders on Free Products [165] 6.1. The Vinogradov Theorem [165] 6.2. Free Products with Amalgamation [169] 6.3. Right-Orderable Groups with Amalgamation [178] Chapter 7. Quasi varieties [181] 7.1. Properties of Quasi varieties [181] 7.2. Model Theory [190] 7.3. Axiomatic Rank [194] 7.4. Locally Indicable Groups [200] 7.5. The Local Indicability of Extensions [205] 7.6. Lattice of Quasi varieties [207] Chapter 8. Semilinearly Ordered Groups [217] 8.1. Definitions [218] 8.2. Basic Properties [223] 8.3. Convex Subgroups [226] 8.4. Constructions [232] References [239] Subject Index [245] Author Index [249]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 06 K83 (Browse shelf) | Available | A-7730 |
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| 06 G773g General lattice theory / | 06 H194 Lectures on Boolean algebras / | 06 K61 Transformations on lattices and structures of logic / | 06 K83 Right-ordered groups / | 06 L364 Lattice theory / | 06 M184 Theory of symmetric lattices / | 06 M184k Kontinuierliche Geometrien / |
Incluye referencias bibliográficas (p. 239-244) e índices.
Chapter 1. Introduction [1] --
1.1. Partially Ordered Sets [1] --
1.2. Lattices [4] --
1.3. Properties of Lattices [7] --
1.4. Orders on Groups [12] --
1.5. Positive Cones [15] --
1.6. Basic Notions [19] --
Chapter 2. Systems of Convex Subgroups [29] --
2.1. General Properties [29] --
2.2. Archimedean Groups [33] --
2.3. Totally Ordered Groups [35] --
2.4. Conradian Groups [37] --
Chapter 3. Orderability Conditions [45] --
3.1. Semigroup Conditions [45] --
3.2. Sufficient Conditions [49] --
3.3. Group Conditions for Total Orderability [52] --
3.4. Groups of Automorphisms [57] --
3.5. Connection with Totally Ordered Groups [59] --
3.6. Fully Orderable Groups [62] --
Chapter 4. Groups of Order Automorphisms [73] --
4.1. Preliminaries [73] --
4.2. Wreath Products [85] --
4.3. Order Types of Right-Ordered Groups [97] --
4.4. The Chehata Groups and the Dlab Groups [100] --
4.5. Embeddings [113] --
Chapter 5. Relatively Convex Subgroups [121] --
5.1. Orderable Representations [121] --
5.2. A Finite Number of Right Orders [132] --
5.3. A Finite Number of Total Orders [142] --
5.4. Center of Right-Ordered Groups [148] --
5.5. Criteria for Orderability [153] --
5.6. Centers of “Small” Subgroups [157] --
Chapter 6. Orders on Free Products [165] --
6.1. The Vinogradov Theorem [165] --
6.2. Free Products with Amalgamation [169] --
6.3. Right-Orderable Groups with Amalgamation [178] --
Chapter 7. Quasi varieties [181] --
7.1. Properties of Quasi varieties [181] --
7.2. Model Theory [190] --
7.3. Axiomatic Rank [194] --
7.4. Locally Indicable Groups [200] --
7.5. The Local Indicability of Extensions [205] --
7.6. Lattice of Quasi varieties [207] --
Chapter 8. Semilinearly Ordered Groups [217] --
8.1. Definitions [218] --
8.2. Basic Properties [223] --
8.3. Convex Subgroups [226] --
8.4. Constructions [232] --
References [239] --
Subject Index [245] --
Author Index [249] --
MR, 97h:06024a
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