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Suzuki M. — Group Theory II
Suzuki M. — Group Theory II



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Название: Group Theory II

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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 621

Добавлена в каталог: 18.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A \times B$ Lemma      9
$S_{\pi}$-subgroup      107
$\mathcal{F}$-conjugate      144
$\Omega$-subgroup      114
$\pi$-separable group      168
$\pi$-solvable group      168
$\sigma$-transposition      574
2-component      454 2
2-generated core      520
2-layer      454 2
2-local p-rank      607 2
2-rank      515
3-Transposition      564
Abelian group      144
Absolute point      557
Alperin      61 145 165 349 525
Aschbacher      409 410 445 525 566 574 603 604 605 607 608 609 610
Automorphism      46
Avoidance-covering property      116
B-conjecture      457
Baer      43
Balanced group      520
Bender      132 372 391 418 458 474 498 514 517 582
Blackburn      12 32 66 413
Block of a design      554
Block of a permutation group      549
Block of a representation      316
Bombieri      517
Brauer      120 122 273 291 306 317 348 419 494 582
Brauer character      273
Brauer correspondence      317
Brauer — Fowler Lemma      122
Brauer — Fowler Theorem      123
Brauer — Fowler, method of      120
Brauer — Suzuki — Wall Theorem      497
Buekenhout      560
Burnside      65 85 108 131 143 216 223 321 356
Burnside, lemma of      131 143
Burnside’s Theorem      143 216 223
Carter      35
Carter subgroup      35
Cc-subgroup      372
Central character      271
Central chief factor      116
Central extension      246
Central product      139
Central series      13
Central series, lower central series      13
Central series, upper central series      89
CHARACTER      265
Character, generalized character      268
Characteristic subgroup      50
Chief factor      116 231
Chief series      90
Chunikhin      175
Class function      267
Class of a nilpotent group      89
Classical involution      605
Classification problem      418
Clifford’s theorem      264
CLIQUE      561
Commutator      1 6 119
Commutator subgroup      2 4
Commutator, higher commutator      4
Commutator, higher, commutator subgroup      13
Complementary graph      566
complete      472
Completely reducible      261
Component of a group      450
Component of a representation      261
Component type, a simple group of      519
Conjugacy functor      148
Conjugate representation      263
Conjugation family      145
Contain the fusion      147
Contain the strong fusion      151
Contraction      568
Control      151
Conway      547
Core-separated      592
Coset      19
Cyclic group      16
Dade      36 277
Degree of a representation      259
Derived group*      2 119
Derived series      119
Design      554
Diagonal automorphism      511
Dickson      202 352 445
Dihedral group      8
Direct product      127
Direct sum of representations      261
E-group      468
Eccentric chief factor      116
Elementary Abelian group      159
Elementary, subgroup      268
Equivalent representations      261
Exceptional character      285
EXPONENT      61
Extraspecial p-group      67
F*-group      469
Factor      116
Feit      61 95 168 258 290 305 356 369 389 419 610
Feit — Thompson theorem      356
Field automorphism      511
Finite p-group      54
Finite solvable group      100
Fischer      36 409 565 574 575
Fischer graph      409 569
Fischer subgroup      36
Fitting length      118
Fitting subgroup      27
Fixed-point-free automorphism      212
Focal subgroup      141
Frattini subgroup      92
Free group*      166
Frobenius      265 275
Frobenius group      275
Frobenius kernel      280
Frobenius subgroup      275
Fully invariant      52
Fuse, fusion      127 138
Gaschuetz      35 36 162 351
Generalized character      268
Generalized decomposition, number      274
Generalized Fitting subgroup      452
Generalized quadrangle      560
Generalized quaternion group      259
Generator*      12
Gilman      610
Glauberman      81 147 154 191 203 225 242 310 315 321 328 474 517 601
Glauberman, Replacement Theorem of Thompson — GIauberman      81
Glauberman, Z* — Theorem      315
Glauberman, ZJ — Theorem      191
Goldschmidt      216 409 474 586 588
Gomi      13 606
Gorenstein      366 457 474 505 513 521 525 608 609 610
Graph      347
Graph automorphism      511
Griess      516 575 610
Group ring      259
Group theoretical property      38
Gruen      163 165
Hall $\pi$-subgroup      107
Hall — Higman theorem      331
Hall, P.      5 19 24 32 33 34 37 46 71 75 92 96 100 105 107 108 113 163 169 171 174 187 255 331 346 356
Hall, P., commutator collecting process      37
Hall, P., formula of P. Hall      37
Hall, P., Three Subgroup Lemma      5
Harada      163 513 514 517 575
Hartley      33 36
Higher commutator      4
Higman, D. G.      141 352 545 552 554
Higman, G.      71 88 331 346 356
Huppert      74 115 291 413
Hypercenter      36
i-th center      89
Incidence matrix      549
Indexial      175
Induced action      71
Induced character      268
Induced representation      262
Induction mapping      270
Involution      120
Irreducible      259
Irreducible character      266
Isaacs      82 244
Isoclinic      93
Isolated element      316
Ito      109 170 267 299
Iwasawa      24
Janko      514 552 608
Kantor      579
Kegel      213
Krull-Remak-Schmidt Theorem      131
Local subgroup      189
Locally nilpotent group      49
Locally P-group      50
Lower central series      13
Lyons      608 610
Mackey Subgroup Theorem      342
MacWilliams      66 514
Magnus      24
Mason      610
Matsuyama      216
Maximal class      32
Maximal subgroup      10
Meta-cyclic      63
Minimal central product      423
Minimal simple group      357 418
Nagao      317
Nilpotent group      89
Nilpotent group, finite nilpotent group      26
Nilpotent length      118
Noncomponent type, a simple group of      519
Nongenerator      34
One-headed group      469
Operator domain      114
Order formula of Thompson      125
Orthogonal      553
Orthogonal group      371
Orthogonality relations      266
p'-group      101
p*-group      458
P- complement      105
P- constrained group      170
P- local subgroup      189
P-block      316
P-group of maximal class      32
p-length      346
P-nilpotent group      154
p-normal      162
p-solvable group      168
P-stable group      190
Parameter of a generalized quadrangle      577
Parameter of a rank three group      548
Perfect group      9
Permutation group      57
Permutation group of rank three      545
Polar space      558
Polarity      553
Poly-cyclic      122
Priifer’s $p^{\infty}$-group      53
primitive      549
Primitive permutation group      549
Principal representation      260
Projection in a subnormal series      174
Projective limit      26
Projective module      340
Quadratic group      190
Quasi-dihedral group      54
Quasisimple group      446
Radical      29
Rank of a permutation group      544
Rank of a polar space      558
Rank of a Shult space      561
Rank three permutation group      545
Reciprocity theorem      265
Reducible      259
Reduction (mod p)      273
Ree      512
Regular p-group      45
Regular representation      260
Replacement Theorem      81
Representation      258
Representation group      252
Residually finite p-group      25
Restriction      262
Robinson      52
Romanovskii      188
Roquette      157
Schreier      88 179 182 330 465
Schur multiplier*      249
Scott      610
Second Main Theorem on p-blocks      317
Section      152
Section Conjugacy functor      152
Seitz      445 605 610
Self-centralizing subgroup      80
Semidirect product      68
Semisimple group      446
Sesquilinear form      555
Shult      409 410 560 586
Shult space      560
Sibley      291 305
Signalizer      472
Signalizer functor      472
Signalizer Functor Theorem      474
Simple group of Lie type      389
Simple group of Ree type      514
Simple group*      30
Simple group, characteristic two type      541
Simple group, component type      519
Sims      92 552
singular      413
Singular quadruple      247
Smith, F.      607
Smith, S.      607 609 610
Solomon, R.      542
Solvable group      118
Solvable group, finite solvable group      100
Special linear group      73
Special p-group      67
Stabilize      20 197
Standard subgroup      604
Steinberg      512
Strongly closed subgroup      584
Strongly closed subset      224 583
Strongly embedded subgroup      391
Strongly p-embedded      608
Strongly real element      120
Subspace of a polar space      558
Subspace of a Shult space      560
Supersolvable group      114
Suzuki      32 291 306 392 413 418 494 512
Sylow series      186
Sylow system      105
Sylow’s Theorem*      95
Symplectic group      371
System normalizer      105
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