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Suzuki M. — Group Theory I

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Название: Group Theory I

Автор: Suzuki M.

Аннотация:

This is a translation from the Japanese of the second volume (chapters four through six) of my book "Gunron" (Iwanami Shoten, 1978). After discussing the concept of commutators in the fourth chapter, we turn to a discussion of the methods and theorems pertaining to finite groups. The last chapter is intended as an introduction to the recent progress in the theory of simple groups. For the translation, I have kept the main body of the text unchanged, however I have added a few comments in the last chapter in order to inform the readers of the most recent progress.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 400

Добавлена в каталог: 28.10.2010

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Предметный указатель

$S_{p}$ -subgroup      95 191
$\Omega$ -(sub) group      114
$\Omega$ -homomorphism      115
$\Omega$ -invariant      114
$\Omega$ -isomorphism      115
$\phi$ -subgroup      92
$\pi$ -component      101
$\pi$ -element      101
$\pi$ -group      101
$\pi$ -number      101
(B,N)-pair      327
Abelian group      6 144
Abelian group, multiplier of an abelian group      265
Abelian group, torsion-free abelian group      280
Action (on a G-set)      60
Action (on a group)      66 114
Action induced action      71
Additive group      7
adjacency      318
Alternating form      335
Alternating group      293—308
Anti-Hopfian group      54
Apartment      319
Ascending chain condition      125
ASSOCIATED      195 263
Associative law      2
Associative law, general associative law      5
Automorphism      46
Baer      14 233 250 285
Baer sum of extensions      224
Bar resolution      205
Bar-convention      32
Base group of a wreath product      269
Basis Theorem of Burnside      93
Baumslag      278
Bender      105
Bilinear form of a Coxeter system      350
Branch point      364
Brauer      113
Bruhat decomposition      334
Building      319
Burnside      93 105 309
Canonical basis of Chevalley      385
Canonical homomorphism      36
Canonical induced action      71
Canonical mapping      31 166
Canonical representation of a Coxeter system      352
Cauchy      97
Cayley      58
Center      14
Center, i-th center      89
Central extension      246
Central product      137 139
centralizer      13
Chamber      319
Chamber complex      318
Characteristic series      116
Characteristic subgroup      50
Chevalley group      386
Chevalley group of exceptional type      387
Chief series      90
Class equation      63
Class of a nilpotent group      89
Class of a nilpotent group, conjugacy class      12
Classical group      370
Coboundary, cochain, cocycle      207
Cohomology dimension      220
Cohomology group      203
Cohomology group (of a subgroup)      207 213
Cohomology group (of cyclic groups)      220
Cohomology group (of free groups)      218
Cohomology group, (one-dimensional)      207
Cohomology group, (three-dimensional)      223
Cohomology group, (two-dimensional)      201 207
Cohomology group, applications      230
Collineation      31 311
Commutative      6
Commutative diagram      198
Commutative, general commutative law      6
Commutator      28 119
Commutator, commutator subgroup      119
Commute elementwise      52
Complement      230
Complete direct product      134
Complete group      56
Complete wreath product      270
Completely decomposable      135
COMPLEX      317
Complex, complex of rank d      318
Complex, thin complex, thick complex      318
Composite      viii
Composition factor      43
Composition of mappings      viii
Composition series      43 (see also “Characteristic series”)
Composition subgroup      45
Congruence      x
Conjugacy class      12
conjugate      12
Conjugate, conjugate subgroup      14
Conjugate, the number of conjugates      22
Conjugation      46
Connectedness      313 318
Connectedness, (of graph)      349
Conway      391
Core      65
Corestriction      208 224
Correspondence theorem      32 40
Coset      19
Coset enumeration      174
Coxeter      173 340
Coxeter group (system)      340
Coxeter group (system), finite Coxeter system      359 369
Crossed homomorphism      207 243
Cycle decomposition of a permutation      292
Cyclic group      16
Cyclic group, automorphism group      49
Cyclic group, cohomology groups      220
Cyclic group, direct sum of cyclic groups      148 151 163—4
Dedekind law      26
Defining relations      165
Defining relations (of a subgroup)      188
Defining relations, examples      165 173 178 259 297—8 340
Derivation      207
Derived scries, derived subgroup      119
Dickson’s theorem      409
Dihedral group      8 173
Dimension of a projective subspace      310
Direct factor      127
Direct power      276
Direct product      70 127 129 134
Direct sum, direct summand      144
Directly (in-) decomposable      129
Distance      319
Divisible group      148 278
Division theorem      ix
Domain of transitivity      64
Double coset      23
Doubly transitive      see “K-transitive (k=2) ”
Eckmann — Gaschlitz Theorem      209
EDGE      347
Elemcntwise commutative      52
Elementary Abelian group      159
Endomorphism      52
Endomorphism ring      53
Epimorphism      35
Equivalent extension      199
Euler function      21
Even permutation      293
Exact sequence      198
Exchange condition      342

Extension      192
Extension, central extension      246
Extension, extension and cohomology      201 232 233
Extension, split extension      230
Factor group      31
Factor set      193
Faithful      158
Feit — Thompson      188 237
Fermat      21
Field      x
Finite field      xii
Finite group      6
Finite group, finite Coxeter groups      347
Finite group, finite subgroups of SL(2,F)      404
Finitely generated      66
Finitely presented      189
Fischer      391
Flag (space)      313
Folding      322
Frame      311
Frattini subgroup      92
Free Abelian group      150
Free central extension      248
Free group      166
Free group, cohomology of a free group      218
Free group, standard form of an element      169
Free group, Subgroup Theorem      182
Free module      202
Free on a set      149 166
Free product (with amalgamation)      186
Free resolution      202
Free subset      160 280
Frobenius      112
Fully invariant      52
G-invariant (subgroup)      71
G-invariant (subset)      60
G-set      59
Gallagher      59 98
gallery      319
Gaschuetz      209 232 239 244 256
General associative law      5
General commutative law      6
General linear group      73
General wreath product      272
Generalized quaternion group      259
Generate      12
Generated freely      150 166
Generating set      12
Generating set, a generating set of a subgroup      180
Generator      12
Generator, generators and relations      164
Geometry of linear groups      310
Glauberman      244
Goldschmidt      105
Gorenstein      392
Graph      347
Graph, graph of finite irreducible Coxeter groups      359
Green      261
Griess      391
Group      2
Group defined by a set of generators and relations      165
Group of automorphisms      46
Group of automorphisms (of a p-group)      93 239
Group of automorphisms (of the alternating group)      299 301
Group of automorphisms (of the alternating group, degree 6)      299 301
Group of automorphisms (of the symmetric group)      300
Group of automorphisms, examples      49 83 161 325 332
Group of inner automorphisms      47
Group of order 168      107
Group of order p*q      103 104
Group ring over $\mathbf{Z}$       201
Group theoretical property      38
Group, abelian group      6 144 280
Group, cyclic group      16
Group, dihedral group      8 173
Group, finite group      6
Group, free group      166
Group, infinite group      6
Group, nilpotent group      89
Group, permutation group      58
Group, solvable group      118
Group, symmetric group      57 291
Hall, M.      106 390
Hall, P.      86 93 106 237 256 279
Harada      391
Height      282
Held      391
Hermitian form      371
Higman, D. G.      244 391
Higman, G.      59 178 189 192 245 278 390 391
Hirsch      122 126
Hochschild — Serre Theorem      213
Homomorphic image      see “Factor group”
Homomorphism      35
Homomorphism theorem      38 115
Homomorphism, operator homomorphism      115
Hyperplane      76
i-th center      89
Identity      4
Identity matrix      7
Indecomposable      129
Independent      129 134 311
INDEX      16
Induced action      71 114
Inductive set      xi
Infinite group      6
Inflation mapping      213
Injective Abelian group      162
Inner automorphism      46
Internal direct product      129
Internal semidirect product      69
Intersection      11
Invariant      60 371
Invariants of an Abelian group      147
Inverse      4
Irreducible action      72 158
Irreducible central extension      252
Irreducible Coxeter system      350
Isoclinism      256
Isomorphic scries      117
Isomorphism      35
Isomorphism class      35
Isomorphism Theorem (First)      41
Isomorphism Theorem (for $\Omega$ -groups)      115
Isomorphism Theorem (Second)      42
Isotropic      378 382
Iwasawa      81 339
Janko      390 391
Jonsson      287
Jordan — Hoelder theorem      43 117
k-transitive      312
Kaloujnine — Krasner Theorem      272
Kernel      35
Krull — Remak — Schmidt Theorem      131
Lagrange      21
Left coset      16
Length of a gallery      319
Length of a series      114
Length of an clement of a Weyl group      329
Length of an orbit      60
Leon      391
Lie type      387
Lifting      246
Linear group      73
Linear group, geometry of linear groups      310
Linearly ordered xi      18
Lyndon      216 228
Lyons      391
Mathieu group      390
Matrix representing a form      372

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