Analytic Pro-P GroupsCambridge University Press, 2003 M09 18 - 388 páginas The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers. |
Contenido
Profinite groups and pro𝓹 groups | 15 |
12 Pro𝓹 groups | 22 |
13 Procyclic groups | 29 |
Exercises | 31 |
Powerful 𝓹groups | 37 |
Exercises | 45 |
Pro𝓹 groups of finite rank | 48 |
32 Pro𝓹 groups of finite rank | 51 |
Exercises | 203 |
Finitely generated groups 𝓹adic analytic groups and Poincaré series | 206 |
Lie theory | 213 |
92 Analytic structures | 217 |
93 Subgroups quotients extensions | 220 |
94 Powerful Lie algebras | 221 |
95 Analytic groups and their Lie algebras | 228 |
Exercises | 235 |
33 Characterisations of finite rank | 52 |
Exercises | 58 |
Uniformly powerful groups | 61 |
42 Multiplicative structure | 64 |
43 Additive structure | 65 |
44 On the structure of powerful pro𝓹 groups | 70 |
45 The Lie algebra | 75 |
46 Generators and relations | 78 |
Exercises | 83 |
Automorphism groups | 87 |
52 The automorphism group of a profinite group | 89 |
53 Automorphism groups of pro𝓹 groups | 91 |
54 Finite extensions | 92 |
Exercises | 96 |
pro𝓹 groups of finite rank | 97 |
Analytic groups | 99 |
Normed algebras | 101 |
62 Sequences and series | 104 |
63 Strictly analytic functions | 108 |
64 Commuting indeterminates | 117 |
65 The CampbellHausdorff formula | 122 |
66 Power series over pro𝓹 rings | 129 |
Exercises | 134 |
The group algebra | 138 |
72 The Lie algebra | 148 |
73 Linear representations | 153 |
74 The completed group algebra | 155 |
Exercises | 166 |
Linearity criteria | 171 |
𝓹adic analytic groups | 178 |
82 𝓹adic analytic groups | 185 |
83 Uniform pro𝓹 groups | 189 |
84 Standard groups | 193 |
Further topics | 241 |
Pro𝓹 groups of finite coclass | 243 |
101 Coclass and rank | 245 |
102 The case 𝓹 2 | 248 |
103 The dimension | 250 |
104 Solubility | 256 |
105 Two theorems about Lie algebras | 262 |
Exercises | 267 |
Dimension subgroup methods | 270 |
112 Commutator identities | 273 |
113 The main results | 282 |
114 Index growth | 285 |
Exercises | 289 |
Some graded algebras | 291 |
121 Restricted Lie algebras | 292 |
122 Theorems of Jennings and Lazard | 298 |
lalternative des gocha | 306 |
Exercises | 310 |
The GolodShafarevich inequality | 311 |
Groups of subexponential growth | 319 |
Analytic groups over pro𝓹 rings | 322 |
132 Standard groups | 330 |
133 The Lie algebra | 339 |
134 The graded Lie algebra | 343 |
135 𝑅perfect groups | 344 |
136 On the concept of an analytic function | 347 |
Exercises | 350 |
Appendix A The HallPetrescu formula | 355 |
Appendix B Topological groups | 358 |
| 362 | |
| 366 | |
Otras ediciones - Ver todas
Analytic Pro-P Groups J. D. Dixon,M. P. F. Du Sautoy,A. Mann,D. Segal Sin vista previa disponible - 1999 |
Términos y frases comunes
abelian analytic function atlas automorphism Cauchy sequence Chapter chart closed subgroup commutative compact converges Corollary Deduce defined denotes dimension dimr elements epimorphism Exercise exists finite index finite p-group finite rank finitely generated pro-p formal group law formal power series G has finite G is finitely G₁ Gi+1 Gn+1 group algebra group G group of finite H₁ hence Hint homomorphism implies induces integral domain inverse limit isomorphism Lemma Lemma Let Let G linear manifold structure N₁ neighbourhood nilpotent norm normal subgroup open in G open normal subgroup p-adic analytic group polynomial positive integer powerful p-group profinite group Proof Let Proposition Let prove Qp-algebra R-analytic R-standard result follows sequence standard group subgroup H subgroup of G Suppose Theorem Let topological group torsion-free uniform pro-p group uniserial write