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| Авторизация |
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| Wilson J.S. — Profinite groups |
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| Предметный указатель |
 13
 13
Algebra 114
Algebra, cohomology 201
Algebra, exterior 227
Algebra, formal power series 120
Algebra, graded 154 ff.
Algebra, group 115
Algebra, Magnus 137
Algebra, profinite 115
Associated graded module, ring 151
Augmentation ideal, map 117
Augmentation-preserving morphism 184
Automorphism group of field extension 47 ff.
Automorphism group of profinite group 52
Baire's category theorem 45
Bar resolution 185—187
Base (for a topology) 1
Basis of a free group 73
Basis of a free module 122
Brauer group 199
Brumer, theorem of 217 ff.
Carter subgroup 45 143
Cartesian product 3
Cauchy sequence 31
centralizer 9
Characteristic subgroup 148
Class (of finite groups) 17
Class (of finite groups), closed for direct products 18
Class (of finite groups), closed for extensions 37
Class (of finite groups), closed for quotients, subgroups 18
Closed set, closure 1
Coboundary 98 165
Cochain 164
Cocycle 97 165
Cofinal subset 29
Cohomological dimension 210 ff.
Cohomological dimension, groups of dimension 1 213
Cohomological dimension, groups of dimension 2 217 ff. 249
Cohomology algebra 201
Cohomology group, definition by cocycles 98 165
Cohomology group, definition by resolutions 181 ff.
Cohomology group, from finite quotients 177 ff. 189
Coinduced module 171 188
Coinduced module, dual of 219
Compact space 1
Compatible pair 166
Complement (to a subgroup) 22
Completed exterior power, square 131 247 255
Completed group algebra 115
Completed group algebra of a free abelian pro-p group 260
Completed group algebra of a free pro-p group 119 ff.
Completed tensor product of modules 129
Completion 24 ff.
Completion of  26 ff.
Completion of abstract free group 72 81
Completion of polynomial algebra 32
Completion pro-C, profinite, pro-p 26
Complex (of modules) 181
Complex (of modules), augmented 183
Connecting homomorphism 170
Continuous map 2
Contracting homotopy 183
Convergent (to 1 or 0), map 68 122
Convergent (to 1 or 0), set 54
Countably based 54
Cross-section 20
Cup product 200 ff. 252
Deficiency of a pro-p group 242 272
Deficiency of an abstract group 242
Demushkin group 249 ff. 272
Dense subset 1
Derivation 101 165
Derived group 60
Dimension shifting 176—177
Direct limit, system 102
Directed set 11
Discrete module 96-7
Duality 105 ff.
Eckmann — Shapiro Lemma 191—192
Embedding theorem 55—56 63—64 66 67 260
Exact sequence 167
Extension of fields 47 ff.
Extension of groups 97 ff. 244
Extension, split 97
Exterior algebra 227
Exterior power, square 131 247 255
Exterior power, square, diagonal action on 247
Extra-powerful pro-p group 148
Feit — Thompson theorem 146 188
Filter 4
Filter base 17
Filtered module 150 ff. 222
Filtration 150 ff.
Filtration-preserving homomorphism 150
Finite presentation 238 ff.
Finite presentation, cobomological criterion for 242
Finite rank 138
Finite rank, abelian profinite groups of 140
Finite rank, pro-p groups of 147 ff.
Finite rank, soluble profinite groups of 139 ff.
Finite rank, soluble profinite groups of, characterization by abelian subgroups 142
Finitely generated profinite group 54
Finitely generated profinite group, determined by finite images 58
Finitely generated profinite module 117
Fitting subgroup 146
Five-term sequence 196 ff.
Fixed-point-free automorphism 43
Formal power series algebra in commuting indeterminates 260
Formal power series algebra in non-commuting indeterminates 120 ff. 137 260 264
Formal power series algebra in one indeterminate 32 65—66
Frattini argument 36
Frattini series, lower 149
Frattini subgroup  41 46
Free module 122 ff.
Free module, dual of 219
Free pro-p group 68 121 250
Free product 92
Free profinite group 68 ff.
Free profinite group, basis of 73
Free profinite group, characterizations of 72 85 92
Free profinite group, every profinite group an image 77
Free profinite group, examples as Galois groups 69 93 214
Free profinite group, rank of 73
Free profinite group, subgroups of 77 83 93
Galois extension, Galois group 47 ff.
General linear group  32 147
Generate topological 53
Generating set 53
Golod — Shafarevich inequality, theorem 264 ff.
Graded module, ring 150 222
Grading 150
Hall subgroup 37
Hausdorff space 1
Homeomorphism 3
Homology groups of a complex 181
Homology groups of a profinite group 207—208
Homotopy equivalence 182
Index (of a subgroup) 34
Inflation map 194 ff.
Inverse limit 11 ff.
Inverse limit, non-emptiness of 14 29
Inverse system 11
Koszul complex 202—204
| Krull topology 52
Lagrange's theorem 35
Lazard, theorems of 150 163 227
Limit of Cauchy sequence 31
Limit, direct 102
Limit, inverse 11
Local ring 126
Lower central series 137
Lubotzky and Mann, theorems of 150
Magnus algebra 137
Max, maximal condition 163
max-n 245 ff. 268—269 272
Mel'nikov, theorem of 85
Metabelian group 32 260
Metric, light-invariant 64
Module, comduced 171 ff.
Module, discrete 96-7
Module, filtered 150 ff. 222
Module, free 122
Module, graded 150 ff. 222
Module, Noetherian 153
Module, profinite 95-6 117
Module, t-free 127
Module, topological 94 ff.
Module, topologically free 127
Morphism (of complexes) 182
Morphism (of complexes), augmentation-preserving 184
Neighbourhood 1
Nielsen — Schreier theorem 82
Nilpotent group 39
Noetherian module, ring 153 246
normalizer 9
Nottingham group 66 67
Open set 1
Order of a profinite group 34
Order of an element 34
p-adic analytic group 150
p-adic integers 26
p-Frattini subgroup  42
p-saturable group 149
p-Sylow subgroup 35
Poincare duality group 227 ff. 249
Polynomial algebra 160 202
Polynomial algebra, resolution for 202-4
Pontryagin duality 105 ff. 207 219
Pontryagin duality, determines exact contravariant functors 110
Powerful prop group 148
Presentation, of a pro-p group 238 ff.
Pro-C group 18
Pro-p group 18 147 154 217 238
Pro-p group of finite rank 138 147 245
Pro-p group, extra-powerful 148
Pro-p group, p-saturable 149
Pro-p group, powerful 148
Pro-p group, uniform 149
Procyclic group 18 31
Product of spaces 3
Product of subgroups of a group 32
Product of subsets of a group 6
Product, semidirect, of groups 22
Product, tensor of complexes 201 ff.
Product, tensor of modules 129 ff.
Product, wreath of groups 61 91
Profinite group, characterizations of 17 ff. 51
Profinite group, countably based 54
Profinite group, finitely generated 54
Profinite group, free 68 ff.
Profinite group, projective 74 ff. 213
Profinite module for a group 95—96
Profinite module for a ring 117
Projective group 74 ff. 213
Projective group, subgroups of 77 ff.
Projective limit 33
Projective module 123
Projective module, is summand of a free module 125
Projector 44—45
Pronilpotent group 40
Prosoluble group 38
Quotient space 3
Radical (of a module) 124
Rank of a free pro-C group 73
Rank of a profinite group 138
Residually finite group 26 31 32
Resolution 181 ff.
Resolution, bar 185—187
Resolution, free 183 222
Resolution, projective 183
Resolution, split 183
Resolution, t-free 183
Restriction map (in cohomology) 193 ff.
Right exactness of pro-C completion 31
Right exactness of tensor product 136
Romanovskii, theorem of 242
Schur — Zassenhaus theorem 38 177
Semidirect product 22
Sequence, Cauchy 31
Sequence, five-term 196 ff.
Sequence, long exact 167 ff.
Sequence, short exact 168
Sequence, well-adjusted 168
Serre, lemma of 224
Serre, theorems of 61 213
Soluble group 37 139
Special linear group  32
Split extension 97
Steinitz number 34 46
Subgroup (of profinite group), abstract of finite index 45 61 65 66
Subgroup (of profinite group), characteristic 148
Subgroup (of profinite group), closed, open 6 ff. 19
Subgroup (of profinite group), derived 60
Subgroup (of profinite group), Hall 37
Subgroup (of profinite group), of projective group 77 ff.
Subgroup (of profinite group), Sylow 36
Subspace (of topological space) 1
Sylow subgroup 36
Sylow's Theorems 36
t-free module 127
Tensor product of completed group algebras 136
Tensor product of complexes 201 ff.
Tensor product of maps 132
Tensor product of modules 129 ff.
Thompson, theorem of 42
Topological generation (of profinite group) 53
Topological group 6 ff.
Topological module 94 ff.
Topological space 1 ff.
Topological space, base for 1
Topological space, compact 1
Topological space, connected 1
Topological space, countably based 54
Topological space, discrete 1
Topological space, hausdorff 1
Topological space, totally disconnected 2
Topologically free module 127 ff.
Torsion group 45
Transversal 20
Tychonoff's theorem 4-5
Ultrafilter 5 65
Uniform pro-p group 149
Upper central series 39
Weight function for a filtration 150
Weight of a profinite group 84
Wreath product 61 91
Zorn's lemma 4
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