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A foreword to the English edition | ||
A couple of words about groups | 1 | |
Introduction | 3 | |
Ch. 1 | Chain. The chain condition for stable groups | 11 |
1.1 | Stable groups; examples | 11 |
1.2 | The order property | 13 |
1.3 | Chain conditions on subgroups | 14 |
1.4 | Connected components | 16 |
1.5 | Omega-categorical stable groups | 18 |
1.6 | Historic and bibliographic notes | 23 |
Ch. 2 | Structure. Model-theoretic analysis of groups of finite Morley rank | 25 |
2.1 | Generics | 25 |
2.2 | Indecomposable sets; Zil'ber's Theorem | 27 |
2.3 | Lascar analysis of a group of finite Morley rank | 29 |
2.4 | Borovik groups and groups of finite Morley rank | 32 |
2.5 | Binding groups | 35 |
2.6 | Hrushovski analysis | 40 |
2.7 | Historic and bibliographic notes | 43 |
Ch. 3 | Fields. Algebraic properties of groups of finite Morley rank | 45 |
3.1 | Fields of finite Morley rank | 45 |
3.2 | Action of an abelian group on an abelian group | 48 |
3.3 | Minimal groups | 50 |
3.4 | Commutators | 53 |
3.5 | Solvable groups | 56 |
3.6 | Semisimple groups | 58 |
3.7 | Action of a group on a strongly minimal set | 60 |
3.8 | Bad groups | 63 |
3.9 | Historic and bibliographic notes | 68 |
Ch. 4 | Geometry. Introduction to algebraic groups | 69 |
4.1 | Constructible groups | 69 |
4.2 | The Zariski closed sets | 71 |
4.3 | Morphisms and constructible functions | 75 |
4.4 | Varieties | 78 |
4.5 | Alegbraic groups; Weil-Hrushovski theorem | 81 |
4.6 | Linear groups: Rosenlicht's theorem | 86 |
4.7 | The Borel Tits theorem | 88 |
4.8 | Historic and bibliographic notes | 91 |
Ch. 5 | Generics. The reconstruction of a stable group from its generic fragments | 93 |
5.1 | Generic types | 93 |
5.2 | The stratified order | 96 |
5.3 | The superstable case | 99 |
5.4 | Infinitely definable groups | 100 |
5.5 | Unidimensional theories | 103 |
5.6 | Groups given generically | 104 |
5.7 | Historic and bibliographic notes | 105 |
Ch. 6 | Rank. Superstable groups | 107 |
6.1 | Lascar inequalities | 107 |
6.2 | Berline Lascar decomposition | 108 |
6.3 | Superstable fields | 112 |
6.4 | Historic and bibliographic notes | 113 |
Ch. 7 | Weight. The last trick for shining in the salons | 115 |
7.1 | Groups and fields with regular generic types | 115 |
7.2 | Hrushovski analysis | 116 |
7.3 | Internal groups of small weight | 120 |
7.4 | Historic and bibliographic notes | 121 |
Bibliography | 123 | |
Index | 125 | |
Postscript: Thirteen years later | 127 |
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Add Stable Groups, This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemp, Stable Groups to the inventory that you are selling on WonderClubX
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Add Stable Groups, This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemp, Stable Groups to your collection on WonderClub |