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R.D.Carmichael — Introduction to the Theory of Groups of Finite Order
R.D.Carmichael — Introduction to the Theory of Groups of Finite Order

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Название: Introduction to the Theory of Groups of Finite Order

Автор: R.D.Carmichael

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 447

Добавлена в каталог: 15.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\phi$-subgroup      82 83 84 163
Abelian groups      30 52 66 69 70 73 83 84 98—119 289—322
Abstract groups      31—36 166—187
Abstractly identical fields      250 251 260
Abstractly identical groups      33
Additive group      243 245
Adjoint configurations      435
Algebras A[s]      396
Algebras of doubly transitive groups      395—414
Alternating group of degree 4      34—36 42 64 65
Alternating groups      20 21 31 38 153 169 172 176 185
Analytical representations      108 263 289 295
Array, rectangular      44
Associated configurations      415
Associative law      6 16
Belonging to a field      246
Belonging to a group      21
Blichfeldt, H. F.      64 66 68
Bocher, Maxime      4
Box porism      417
Burnside, W.      197 234 271
Bussey, W. H.      323 327 345
Central      47 66 83 87
Central factor-group      120
Characteristic determinant      192
Characteristic equation      192
Characteristic subgroup      81 83 84
Characteristics      193 210 223
Chief-series      97
Circular permutation      7 14 15
class      3
Co-ordinates in groups      290
Coble, A. B.      417 418
Collineation      359
Collineation group $C(k, {p}^{n})$      360 362
Collineation groups      355—394
Combination, rules of      4
Commutative      13 27
Commutative group      30
Commutator subgroup      29 36 37 38 39 53 82 88 127
Commutator-series      97
Commutators      13 14 28 37 39 41 42 53 70 73
Complementary configurations      415
Complete $\lambda-\mu-\nu-$configurations      433 437
Complete 2-2-k-configurations      42 434 437
Complete conjugate set      47 71
Complete groups      81 83 95 96
Completely reduced form      208
Completely reduced sets      200
Completely reducible      200
Composite group      48 69 71 226
Composition of groups      204 206
Composition-factor-groups      89
Composition-factors      89
Composition-series      88 96 97
Compound of two groups      204 205 206
configurations      346 415—441
Conformal groups      32 38 41 53 70 71
Congruent polynomials      252
Conjoint groups      57
Conjugate elements      46
Conjugate subgroups      47
Conjugate-imaginary groups      191 198
Conjugate-imaginary transformations      191
CYCLE      11
Cyclic groups      29 36 38 52 83 104
Cyclic permutation      7
Defining relations      34 166—187
Definite Hermitian form      196
Degree      5 19
Degree of transitivity      139 148
Derived groups      29
Desargues      337
Dickson, L. E.      64 66 68 285 315 396 403 404 413
Dicyclic groups      182 183
Dihedral groups      181 183
Direct product      52
Double holomorph      81
Double modulus      252
Doubly transitive groups      266 267 272 286 305 306 310 313 319 320 337 363 372 375 395—414
Doubly transitive groups of degree n and order n(n— 1)      143—147
Duality, principle of      330 334 337
Element      3
Elements of a group      26—28
Emch, A.      440
Empirical theorems      315—317
Equality      16
Equivalent representations      207
Euclidean geometries      329
Even permutation      9 10 19 20
Factor-groups      84—88
Fields      242—288
Fields within a field      260
Finite fields      242—288
Finite geometries      323—354 407—413
Finite group      17
Frobenius, theorem of      92 126
Fundamental theorems      44 55 58 66 68
Galois field defined      255
Galois fields      242—288
Galois fields, existence of      256
General isomorphism      74 75 85
General linear homogeneous group      291
Generators      30 31 66 82
Geometric set of subgroups      291 328 344
Geometries, finite      323—354 407 408
Group characteristics      210 223
Group of degree 11 and order 660      24 25 65
Group of degree 7 and order 168      21—22 24 25 31 53 65 84
Group of inner isomorphisms      78 87
Group of isomorphisms      78 83 84 95 289—322
Group of order 4n + 2      94
Group property      16
Group, definition of      15—19 395
Groups of degree 13      40 72
Groups of degree 15      43 162 165
Groups of degree 16      42 43 165
Groups of degree 4      151
Groups of degree 5      151
Groups of linear transformations      188—241
Groups of order ${p}^{2}$      65 69
Groups of order ${p}^{2}q$      70
Groups of order ${p}^{3}$      69 71 73
Groups of order 60      72
Groups of order 6p      72
Groups of order 8      36 37 38 94 134
Groups of order p(p - 1)      40 41 42
Groups of order pq      64 95
Groups of orders 1-15      69
Groups of orders 16-26      73
Groups of prime degree      234 239 387 389
Groups of prime order      45
Groups {s, t} such that ${s}^{2}={t}^{2}$      177
Hamiltonian groups      113—116 117
Hermitian forms      196
Hilton, H.      113
Holomorph      79—81 83 84 163 303
Identical element      16
Identical isomorphism      76
Identical permutation      5
Identical representation      207
Identity      16 17 190 395
Imprimitive groups      159
Imprimitive systems      160
Index of subgroup      45
Infinite group      17
Inner isomorphism      78 87
Integral elements of $A[{p}^{n}]$      404
Integral marks      244 261
Intransitive groups      54 158 162
Invariance under group      20 21
Invariant      46 47
Inverse      6 16 189 396
Irreducible components      208
Irreducible equation      246
Irreducible groups      200
Irreducible in a field      246
Irreducible modulo p      253
Irreducible representations      207
Isomorphism      31 74
Isomorphism of algebras      402
Isomorphism, general      74 75 85
Isomorphisms of a group with itself      76—79
Isomorphisms of Abelian groups      107—113 289—322
Isomorphisms of cyclic groups      104
Jordan, C.      146
Kronecker, L.      229
Lagrange      44
Linear fractional groups in one variable      266
Linear groups in one variable      265
Linear homogeneous group      111
Linear nonhomogeneous group      111
Linear transformations in A[s]      400
Magic squares      393
marks      242 396
Mathematical system      4
Mathieu groups      151 165 263 283 288 431
Matrix of substitution      188
Maximal self-conjugate subgroup      82
Maximal subgroup      82
Maximum self-conjugate subgroup      82
Maximum subgroup      82
Metacyclic groups      184
Miller, G. A.      64 66 68 150 433
Modulus double      252
Monomial transformation      193
Multiple isomorphism      75
Multiple transitivity      139 143
Multiplication      6 16 189
Multiplication (transformation)      193
Multiplication table      32
Multiplicative group      243 248
Multiplier      192 193
Multiply transitive groups      143 387 389 392 441
Netto, E.      425 433
Non-Abelian group      30
Noncommutative group      30
Noncyclic group      29
Nonequivalent representations      207
Nonzero definite      198
normal      46 47
Normalizer of element      49
Normalizer of subgroup      49
Not-square marks      262
Object, mathematical      3
Octic group      20 24 30 31 36 37 54 176 373
Odd permutation      9 19
Order      10 11 17 27
Order of a field      243
Order of a mark      247
Outer isomorphism      78
Pappus      339
Partitions of a group      84
Perfect group      29 38 94
Permutable      13 27
Permutation groups      19 22—23 138—165
permutations      5
Post-multiplication      56
Power      10 11 14 26 27
Pre-multiplication      56
Prime-power groups      30 67 69 73 120—137
Primitive groups      159 162 163 165 372 375
Primitive groups of degree 8      165
Primitive groups off low degree      392
Primitive mark      248 250 288
PRODUCT      5 16 189
Projective geometries      323
Projective group $P(k, {p}^{n})$      355
Projective transformations      355
Proper subgroup      28
Punct      331
Quadrangle      341
Quadruple systems      25 26 72 73 429 436 440
Quadruples      348 351 352 353 354
Quadruply transitive groups      389 see
Quaternion group      113 117
Quintuple systems      432
Quintuples      354
Quintuply transitive groups      see “Mathieu groups”
Quotient      85
Quotient group      85
Rect      331
rectangular array      44
Reduced sets      200
Reducible groups      200
Reducible modulo p      253
Regular groups      54 55 217
Regular permutations      11 39
Representation as a regular group      53
Representation as a transitive group      155
Representation of a finite group      206
Representations of permutations      263
Roots of unity      228 287
Rules of combination      4
Schur, I.      234
Self-adjoint configurations      436
Self-conjugate      46 47
Sextuple systems      431
Similar permutations      12 14
Similarity transformation      193
Simple groups      48 64 71 83 276—283 285
Simple groups of order less than 1, 000, 000      285
Simple isomorphism      31
Simply isomorphic      75
Soluble group      91
Solvable group      91 92 94 97 229
Square marks      262
Standard form of permutation      11
Subalgebra      404
Subfield      260
Subgeometries      334 419
Subgroups      28—29 44 81—83
Subgroups of index 2      52
Subgroups of prime-power order      63
Substitution polynomial      264
Substitutions      5 188
Sylow subgroups      58 63 64 65 66
Sylow's theorem      58
Symmetric group      19 21 24 31 38 154 169—176
Symmetric group of degree 4      64 65
Symmetric group of degree 6      43
Symmetric group of degree n      65
system      3 4
Systems of imprimitivity      160
Tactical configurations      346 415—441
Theorem of Desargues      337
transform      12 13 27 28 47
Transformations, linear      188
Transitive group, representation as      155
Transitive groups      54 139 152 162 163 164 165 229 234 239
Transitive sets      158
Transitivity, degree of      139 148
Transposed transformation      191
Transposition      7
Triple groups      425
Triple systems      21 53 425 436 440 441
Triply transitive groups      147—148 267 272 286 305 306 320 363 372 375 389 413
Type of abelian group      67 98
Veblen, O.      323 327 339 340 345 360 394 407
Weber, H.      236
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