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James G., Liebeck M.W. — Representations and Characters of Groups
James G., Liebeck M.W. — Representations and Characters of Groups

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Название: Representations and Characters of Groups

Авторы: James G., Liebeck M.W.

Аннотация:

This is the second edition of the popular textbook on representation theory of finite groups. The authors have revised the text greatly and included new chapters on Characters of GL(2,q) and Permutations and Characters. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2001

Количество страниц: 466

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_4$      112 130 136 181 308
$A_5$      10 112 116 220 312 359
$A_6$      116 222
$A_7$      223
$A_n$      5 9 11 111 343
$C_n$      2 82 88
$D_{2n}$      2 12 107 181
$F = \mathbb{R}$ or $\mathbb{C}$      3
$F^n$      15
$F_{p,q}$      290
$H \leqslant G$      3
$H \vartriangleright G$      9
$Hom_{\mathbb{C}G}(V, W)$      95 96
$S_4$      44 110 113 180
$S_5$      111 201 262
$S_6$      116 205
$S_7$      223
$S_n$      3 175 254 344
$T_{4n}$      178 187 281 420
$U_{6n}$      178 187 421
$V_{8n}$      178 187 421
$\mathbb{C}$      2
$\mathbb{Z}$      2
Abelian group      3 11 81 82
action      337
Algebra      55 56
Algebraic integer      244 362
Algebraic number      361
Alternating group      5 9 11 111
Antisymmetric part      196 273
Associative      2
Basis      15
Basis, natural      45 54
Bijection      6
Bilinear form      269
Bilinear form, skew-symmetric      269
Bilinear form, symmetric      269
Brauer — Fowler Theorem      278
Burnsides lemma      340
Burnsides Theorem      363 364
centralizer      106
Centre of group      85 107 298
Centre of group algebra      83 114 153
Change of basis      24
CHARACTER      118
Character table      159
Character table, $A_4$      181
Character table, $A_5$      221 359
Character table, $A_6$      359 424
Character table, $C_2 \Times C_2$      415
Character table, $C_2$      160
Character table, $C_3$      160
Character table, $C_4$      412
Character table, $C_n$      82
Character table, $D_6 \Times D_6$      423
Character table, $D_6$      160
Character table, $D_8$      161
Character table, $D_{10}$      415
Character table, $D_{12} \cong S_3 \Times C_2$      207 419
Character table, $D_{2n}$ (n even)      183
Character table, $D_{2n}$ (n odd)      182
Character table, $F_{11, 5}$      433
Character table, $F_{7, 3}$      240 417
Character table, $F_{p, q}$      291
Character table, $Q_8$      416
Character table, $S_4$      180
Character table, $S_5$      201 262
Character table, $S_6$      205
Character table, $T_2$      186
Character table, $T_{4n}$      420
Character table, $U_{6n}$      421
Character table, $V_{24}$      422
Character table, $V_{8n}$      421
Character table, direct product      206
Character table, E of order 18      434
Character table, GL(2,g)      327
Character table, order $p^3$      301
Character table, order 16      305 306 307
Character table, order 27      435
Character table, order < 32      308
Character table, order pq      291
Character table, p-group      300
Character table, PSL(2,11)      443
Character table, PSL(2,7)      318
Character table, PSL(2,8)      445
Character table, SL(2,3)      440
Character table, SL(2,7)      442
Character table, SL(2,q)      445
Character, degree      122 247
Character, faithful      125 195
Character, generalized      355
Character, induced      230 234 236
Character, integer-valued      253
Character, irreducible      119
Character, kernel of      125
Character, linear      122 172 174
Character, permutation      129
Character, product      176 192
Character, real      263
Character, realized over R      265
Character, reducible      119
Character, regular      127 128 150
Character, trivial      122
Class algebra constants      349
Class equation      107
Class function      152
Class sum      114
Cliffords Theorem      216
Complete set      101
Completely reducible      74
composition      2
Composition factor      90
Composition factor, common      91 96
Congruences      259
Conjugacy class      104
conjugate      104 361
Constituent      143 213
Coset      8
Cycle notation      8
Cycle-shape      109
Cyclic group      2 4 12 82 88
Degree      30 122 249
Derived subgroup      173
Diagonalization      83
Dicyclic group $T_{4n}$      178 187 281 420
Dihedral group      2 12 107 181
DIMENSION      15
Direct product      5 206
Direct sum      17 66
Direct sum, external      18
Eigenvalue      24
Eigenvector      24
Endomorphism      20
Equivalent      32 46
Even permutation      5
Expansion-contraction mode      381
External direct sum      18
Factor group      9
Faithful character      125 195
Faithful module      44 56 85
Faithful representation      34
fg      53
FG-homomorphism      61
FG-isomorphism      63
FG-module      see module
FG-submodule      49
Frobenius group      290
Frobenius reciprocity theorem      232
Frobenius — Schur Count of Involutions      277
Function      6
Function, bijective      6
Function, injective      6
Function, invertible      6
Function, surjective      6
General linear group      3
GL(2,q)      324 343
GL(n,F)      3
Group      1
Group algebra      55
Group, abelian      3 11 81 82
Group, alternating      5 9 11 111
Group, cyclic      2 4 12 82 88
Group, dicyclic      178
Group, dihedral      2 12 107 181
Group, factor      9
Group, finite      2
Group, general linear      3
Group, order      2
Group, order pi      302 304
Group, orthogonal      367
Group, projective special linear      312
Group, quaternion      5
Group, rotation      368
Group, simple      10 250 278 311 318 353 363 364
Group, soluble      365
Group, special linear      311
Group, symmetric      3 109 116 175 254
Group, symmetry      368
Homogeneous component      376
Homomorphism      6 10 61
Ideal      256
Ideal, maximal      257
Ideal, proper      257
Index of subgroup      9
Indicator function      273
Induced character      230 234 236
Induced module      226 228
Inner product      134
Involution      277 353
Irreducible character      119
Irreducible module      50 74 79 91
Irreducible representation      50 79
Isomorphism      7 20 63
Kernel      10 19 34 124 125
Lagrange's theorem      9
Lift      169
Linear character      122 173 174
Linear transformation      18
Linearly dependent      15
Linearly independent      15
Maschkes Theorem      70
Matrix      21
Matrix, change of basis      24
Matrix, diagonal      26
Matrix, identity      3 21
Matrix, invertible      23
Matrix, permutation      45
methane      384
Minimal polynomial      361
Module      39
Module, completely reducible      74
Module, faithful      44 85
Module, irreducible      50 79 85
Module, permutation      45 62
Module, reducible      50
Module, regular      56
Module, trivial      43
Natural basis      45 54
Normal modes of vibration      372 373
Normal p-complement      251
Normal subgroup      9 113 171 215 216 217
Odd permutation      5
Orbit      338
Order of G      2
Orthogonal group      367
Orthogonality relations      161
p'-part      256 258
p-group      298
Permutation      3 5
Permutation character      129 340
Permutation matrix      45
Permutation module      45 62 340
Permutation, even      5
Permutation, odd      5
Powers of characters      193
Presentation      3
Primitive root      284
Product of characters      176 192
Projection      27
Projective special linear group      312
PSL(2,11)      321 359
PSL(2,7)      312 318 319 354 359 360
PSL(2,p)      312
q      5 116 177 278 416
Quaternion group      5 116 177 278 416
R      3
Rank      342
Rank-nullity theorem      19
Real character      263
Real conjugacy class      263
Real element      263
Reducible character      119
Reducible module      50
Reducible representation      50
Regular character      127 128 150
Regular module      56
Regular representation      56
Representation      30
Representation, degree      30 249
Representation, equivalent      32
Representation, faithful      34
Representation, irreducible      50
Representation, kernel of      34
Representation, reducible      50
Representation, regular      56
Representation, trivial      34
Representatives      105
Restriction      210
Rotation group      368
Rotation mode      379
Rotation submodule      380 394
Schur s Lemma      78
Simple group      10 250 278 311 318 363 364
Skew-symmetric bilinear form      269
SL(2,3)      319 440
SL(2,7)      320 442
SL(2,p)      311
SL(2,q)      336
Special linear group      311
Stabilizer      339
Subgroup      3 4
Subgroup, cyclic      4
Subgroup, derived      173
Subgroup, generated      4
Subgroup, normal      9 113 215 216 217
Submodule      49
Submodule, irreducible      74
Sylow's theorem      354
Symmetric bilinear form      269
Symmetric group      3 109 116 175
Symmetric part      196 273
Symmetry group      368
Tensor product module      190
Tensor product space      188
Trace      117
Transitive      338 341
Transitivity of induction      229
Translation mode      379
Translation submodule      380 394
Transposition      5
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