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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

Matsumoto      342
Matsuyama      88 105
Maximal condition for subgroups      125
Maximal normal subgroup      33
Maximal subgroup      10
McKay      390 391
McLaughlin      98 391
Mendelsohn      178
Minimal normal subgroup      33 137
Minimal simple group      418
Module      153
Monomorphism      35
Multiplication of matrices      1
Multiplicative group of a field      7
Multiplier      249
Multiply transitive      312
Natural numbers      ix
Neumann, B. H.      192 269 272 277—8
Neumann, P.      59 228 272
Nielscn — Schreier Theorem      181
Nilpotent group      89 (see also “p-group”)
Nondegenerate      335 371
Normal (endomorphism)      53
Normal (subset)      31
Normal subgroup      29
Normalized cochain      206
normalizer      13
Norton      391
Novikov — Adjan Theorem      271
Odd permutation      293
Operation      2
Operator domain      114
Operator group      66
Operator group, induced action on factor groups      71
Operator homomorphism      115
Orbit      60
Order (a relation)      xi
Order of a group      6
Order of an element      16
Ore      34
Orthogonal      372
Orthogonal group      371 375 380
Outer automorphism class group      48
O’Nan      391
p-group      86
p-group, infinite p-group      270
p-subgroup      95
Partially ordered set      xi
Permutation      56
Permutation group      57
Permutation representation      59
Permutation, even (odd) permutation      292
Poly-cyclic (poly-P) group      122
Positive semi-definite      361
Presentation      165
Primary component      149
Primitive central extension      252
Principal crossed homomorphism      207
Principal series      90
Product (of automorphisms)      46
Product (of elements)      2 4
Product (of endomorphisms)      52
Product (of mappings)      viii
Product (of matrices)      1
Product (of motions)      8
Product (of permutations)      56
Product of subgroups (subsets)      24
Product of subgroups (subsets), central product      137
Product of subgroups (subsets), direct product      127
Product of subgroups (subsets), free product      186
Product of subgroups (subsets), semidirect product      68
Product of subgroups (subsets), tensor product      264
Product of subgroups (subsets), wreath product      268
Projection      131
Projective general linear group      312
Projective module      229
Projective representation      263
Projective resolution      229
Projective space      310
Proper subgroup      10
Pure subgroup      162
Quadratic form in characteristic two      380
Quadratic form of a Coxeter system      351
Quaternion group      34 140
Quaternion group, generalized quaternion group      259
Quaternion skew-field      34
Quotient group      see “Factor group”
R-module      153
Rank of a complex      318
Rank of an abelian group      147 150 161 280
Reducible      158
Ree      387 389
Ree group      389
refinement      117
Refinement Theorem      117
Reflection (in an apartment)      324
Reflection group      367
Regular abelian group      156
Regular action      72
Regular representation      58
Relation among generators      164
Relatively prime      ix
Remak — Schmidt — Krull Theorem      131
Representation      59 263
Representation group      252 268
Residually finite      126
Resolution      202
Resolution, projective resolution      229
Resolution, resolution by relations      229
Restricted direct product      134
Restriction      40
Retraction      320
Right coset      16

Ring of endomorphisms      53
Root system      366 385
Rudvalis      391
Schenkman      245
Schmidt      270
Schreier      48 117 181 187
Schreier conjecture      48
Schreier transversal      181
schur      159 235 249—52 264—7 302
Schur multiplier      249
Schur multiplier (of the alternating group)      304
Schur multiplier (of the symmetric group)      301
Schur — Zassenhaus theorem      235
Schur’s lemma      159
Scmidirect product      68
Serre      213 230
Set of coset representatives      see “Transversal”
Simple group      30
Simple group of Lie type      389
Simple group, alternating groups      295
Simple group, simple groups of order less than thousand      310
Simple group, sporadic simple groups      390
Simple group, survey      369
simplex      313
Simply transitive      325
Sims      59 176 391
Skew-field      7
Solvable group      90 118
Special linear group      73
Split extension      230
Sporadic simple groups      389
Stabilizer      61
Stallings — Swan theorem      220
Standard bar resolution      205
Standard embedding      393
Standard form      169 187
Standard wreath product      272
Steinberg group      388
Subcomplex      318
Subgroup      9
Subgroup (of a central product)      143
Subgroup (of a direct product)      140
Subgroup (of a free abelian group)      152
Subgroup (of a free group)      182
Subgroup, characteristic subgroup      50
Subgroup, conjugate subgroup      14
Subgroup, finite subgroups of SL(2,F)      393
Subgroup, maximal subgroup      10
Subgroup, normal subgroup      29
Subgroup, proper subgroup      10
Subgroup, trivial subgroup      10
Subnormal      114 123
subspace      310
SUM      7
Summable endomorphisms      52
Suzuki      334 389 391
Suzuki group      389
Sylow p-subgroup      95
Sylow p-subgroup, the number of Sylow p-subgroups      96 106
Sylow’s Theorem      95
Sylow’s Theorem (for infinite groups)      191
Sylow’s Theorem, (generalizations)      99 238
Symmetric form      375
Symmetric group      57
Symmetric group, (of degree n)      58 291
Symplectic basis      335
Symplectic frame      337
Symplectic group      336 371 373
Tensor product      264
Thick (thin) complex      318
Thompson      105 188 237 391 418
Tits      334 352 389
Tits system      327
Torsion subgroup      148
Torsion-free      148 191
Totally isotropic      335
Transitive      64
Transitive, multiply transitive      312
Transposition      292
Transvection      76
Transversal      21
Transversal, Schreier transversal      181
TREE      364
Trivial $\Gamma$ -module $\mathbf{Z}$       202
Trivial subgroup      10
Twisted wreath product      269
Type of a torsion-free abelian group of rank one      282
Type of a vertex      325
Type of permutations      292
union      29
Unitary group      371 374
Universal Chevalley group      386
Upper central series      89
Vertex of a building      318
Vertex of a graph      347
Waerden, van der      187
Wales      390 391
Wall of a building      319
Walter      392
Weyl group      324 327
Wiegold      261
Wielandt      56 97 125 275
Witt      359 390
Word      170
Word, the word problem      172
Wreath product      268
Wreath product, complete wreath product      270
Wreath product, standard wreath product      272
Wreath product, twisted wreath product      269
Yamazaki      246
Zassenhaus      116 125 235
Zero of a field      xi
Zorn’s Lemma      xi

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