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Holt D.F., Bettina E., Eamonn O. — Handbook of Computational Group Theory
Holt D.F., Bettina E., Eamonn O. — Handbook of Computational Group Theory



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Название: Handbook of Computational Group Theory

Авторы: Holt D.F., Bettina E., Eamonn O.

Аннотация:

This work offers a treatment of fundamental methods and algorithms in computational group theory (CGT) at a level accessible to advanced undergraduates. It develops the theory of algorithms in detail and highlights the connections between the different aspects of CGT and other areas of computer algebra. While acknowledging the importance of the complexity analysis of CGT algorithms, the book's primary focus is on algorithms that perform well in practice rather than on those with the best theoretical complexity. Applications of algorithms demonstrate how CGT fits into the wider world of mathematics and science


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 536

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
ITC (interactive Todd — Coxeter)      170
Ivanyos — Lux extension to Meataxe      235
Ivanyos, G.      235
Jansen, C.      4 236 409
Jerrum, M.      93 147
Johnson, D.L.      353
Jordan — Holder theorem      27
Jordan, C.      81
Jurgensen, H.      354
Kannen, R.      349
Kant      6
Kantor, W.M.      132 144 272 381 384 396
KBMAG      4 425 433 456 466
Kerber, A.      390
Kernel      15
Kernel of a monoid homomorphism      413
Kernel of an action      18
Key, J.D.      145 146
KG-module(s)      49
KG-module(s), absolutely irreducible      50
KG-module(s), centralizing algebra      50
KG-module(s), composition factors      50
KG-module(s), composition series      50
KG-module(s), computing endomorphism algebra      241
KG-module(s), computing homomorphisms of      241
KG-module(s), endomorphism algebra      50
KG-module(s), extension      52
KG-module(s), finding all irreducible      246
KG-module(s), irreducible      49
KG-module(s), simple      49
KG-module(s), testing for absolute irreducibility      237
KG-module(s), testing for indecomposability      242
KG-module(s), testing for irreducibility      230
KG-module(s), testing for isomorphism      244
Kim, A.C.      353
Kleinian group      470
Knot group      352
Knuth — Bendix completion      187 417 420 430 433 440 442 457 458
Knuth — Bendix completion, implementing      422
Knuth, D.E.      68 93 144 417 443
Kolata, G.      144
Kovacs, L.G.      352
Labahn, G.      347
Lagrange's theorem      11
Las Vegas algorithm      68 272
Laue, R.      131 295
Leading exponent      277
LeChenadec, P.      425
Leech, J.      2 149 162
Leedham-Green, C.R.      66 70 235 242 269 271 272 283 284 301 320 364 371 374
Left transversal      12
Lenlex ordering      43
Leon, J.S.      97 115 119 120 204 207
lexicographical ordering      43
Libraries of groups      393
Library, perfect groups      400
Library, primitive permutation groups      394
Library, small groups      402
Library, transitive permutation groups      397
Liebeck, M.      270 395 396
Linear character      263
LLL algorithm      6 349
Lo, E.H.      6 354 364
Locally confluent rewriting system      418
Loehr, N.A.      60
Lookahead      164
Lookahead (coset enumeration)      164
Low-index subgroups algorithm      188 198 326 352 373
Lower central series      29 355
Lower exponent-p central series      355
LowIndexSubgroups      191
Lubeck, F.      347 348
Luks, E., vi      93 109 133 272
Lux, K.      4 235 236 409
Lyons group      2 208 236
Macdonald, I.D.      3 364
Magma      5 17 120 132 146 170 185 189 207 208 220 221 242 244 255 268 326 353 364 373 374 380 383 384 386 393 397 409 410
Magnus      7
Majewski, B.S.      347 349
Maple      5
Mathematica      5
Matrix groups, computing in      264
Matrix groups, computing in large — degree      268
Matthews, K.R.      347
Maximal subgroups      11
Maximal subgroups, computing      322 384
McKay, Brendan D.      6 119
McKay, John      4 255 257 397 400
McShane, G.      470
Meataxe      232
Meataxe algorithm, Ivanyos — Lux extension      235
Meataxe algorithm, vii      4 6 219 230 376 382
Mecky, M.      311
Medvedoff, S.      144
Membership testing      63 66
MERGE      86 157
Miller, C.F. (Ill)      6 149 354
Minimal normal subgroup      26
Minimal polynomial of a matrix, computing      224
Minimal string in rewriting system      421
MinimalBlock      84 86
MinimalPolynomial      226
Minkwitz, T.      148
MLLL algorithm      6 349
Modified coset enumeration      178
Modified coset table      174
Modified Todd — Coxeter procedure      178
ModifiedCoincidence      181
ModifiedDefine      179
ModifiedScan      180
Module homomorphisms computing      241
ModuleHomomorphisms      243
ModuleIsomorphism      245
MOLGEN      392
Monoid      412
Monoid presentation      412 415
Monoid, finitely generated      413
Monoid, finitely presented      415
Monoid, free      415
Monomorphism      15
Monster      4
Monte Carlo algorithm      68 81 142 272
Moori, J.      146
Morrison, K.      144
Mortimer, B.      394 396
Muller, J.      236
Multiplier automaton      451 457 461 465
Murray, S.H., vi      265
n-fold transitive action      22
Nauty      6 119
Nebe, G.      408
Network processor interconnection      148
Neubuser, J.      1—3 5 7 150 170 283 295 304 311 317 373 385
Neumann, B.H.      197 425
Neumann, P.M.      62 132 139 271
Newman, M.F.      3 353 360 364 370 372—374
Newman, M.H.A.      2
Nickel, W.      60 360 364 430
Nielsen — Schreier theorem      43
Niemeyer, A.C.      271 360 364
Nilpotency class      29
Nilpotency verifying      429
Nilpotent group      29
Nilpotent presentation      286
Nilpotent quotient algorithm      364 429
Noetherian rewriting system      418
Nonconstructive recognition algorithm      271
Normal closure      14
Normal closure, computing      73
Normal form for group elements      63 88 276 325 354 411 434
Normal subgroups      14
Normal subgroups, computing      384
NormalClosure      74
NormalFormExponents      102
Normalizer of a subgroup      21
Normalizer of a subgroup, computing      121 314
NormalizingGenerator      100
NormalSubgroup      380
Norton, S.      4 409
Not Knot      470
Novikov, P.S.      1 149
NullSpace      225
Nullspace of a matrix, computing      223
NumberBlocks      106
O'Brien, E.A.      2 3 265 271 353 370—372 374 394 402
O'Nan — Scott theorem      3 142 378 394
Orbit      78
Orbit-stabilizer theorem      19
Orbits of an action      19
Orbits, computing      77 302
Orbits, computing induced action on      105
OrbitStabilizer      79
OrbitSv      80
Order of element      10
Order of element, computing      66 72
Order of group      10
OrderBounded      73
Ordered partition      120 122
Ordered partition, refinement      120
Orthogonal complement      231
Orthogonality relations      258
Ostheimer, G.      311
Out(G)      15
Outer automorphism      15
P-Core      141
p-core, computing      138
p-covering group      357
p-covering group, computing      359
P-CoveringGroup      360
p-group      21
p-group generation algorithm      364
p-group, elementary abelian      11
p-multiplicator      364
P-quotient      362
p-quotient algorithm      3 355 364
p-regular element      247
Padding symbol      442 454
Pak, I.      69 271 384
Panaia, O.      364
Papasoglu, P.      468
Parker, John      470
Parker, Richard A.      4 59 221 230 236 246 271 409 410
Partial base image      113
Partition ordered      120 122
Path compression      86
PC      278
PC-group      278
Perfect groups      28
Perfect groups, library of      400
Permutation      13
Permutation representation      17
Permutation word      93 95
Permutation, even, odd      13
Plesken, W.      246 364 385 400 405 408
Pless, V.      145
Pointwise stabilizer      20
Polycyclic generating sequence      354 426
Polycyclic group      29 273 353 425
Polycyclic group, rewriting system      426
Polycyclic monoid presentation      427
Polycyclic presentation      3 61 273 278 354
Polycyclic presentation, computing      354
Polycyclic presentation, confluent      280
Polycyclic presentation, consistent      280 354 428
Polycyclic presentation, refined      285
Polycyclic quotient algorithm      364 429
Polycyclic relations      278
Polycyclic sequence      99 274 354
Polycyclic sequence induced      291
Polycyclic sequence, canonical      296
Polycyclic series      273
Polycyclic series induced      291
PolycyclicOrbitStabilizer      304
Polynomial Conway      59
Polynomial factorization      226
Polynomial primitive      59
Polynomial-time algorithms      109
Polynomially equivalent algorithms      126
Power      72
Power exponents      278
Power-conjugate presentation      3 355
Power-conjugate presentation, weighted      358
Powers of element, computing      72
Praeger, C.E.      133 137 271 395
Prefix of a word      34
Presentation      202
Presentation of a group      38
Presentation of a group (computing)      199
Presentation of a monoid      412 415
Presentation of a subgroup      41
Presentation of a subgroup (computing)      173
Presentation, abelian group      47
Presentation, nilpotent      286
Presentation, polycyclic      273 278 354
Presentation, simplifying      184
Presentation, supersolvable      288
Primitive action      23 82
Primitive finite field element      59
Primitive permutation groups library of      394
Primitive polynomial      59
Principal derivation      52
PrInitialize      70
PrintElements      110
ProcessDeductions      166
Processor interconnection network      148
Product replacement algorithm      69 97 232
PrRandom      71
Pruning a search tree      113
Quotient groups, representing      62 133 137
Quotient of a monoid      414
QUOTPIC      7 325
R(2, 6)      431
R(d, n)      372
Rabin — Karp string-matching algorithm      441
Rabin, M.O.      1 371
Ramsay, C      2 162 170
Random elements of a group      69 95 97 136 218 272
Random Schreier — Sims algorithm      97 264
Random techniques in CGT      69
Randomized algorithm      67
RandomSchreier      98
RandomStab      81
Rank of free group      34
Recognition algorithm, constructive      271
Recognition algorithm, nonconstructive      271
Redfern, I.      470
Reduced rewriting system      421
Reduced word      35
ReduceToConstantDegree      229
ReduceToSquareFree      228
Rees, S.E.      7 230 271 325 349 371 432 433 456
Refined polycyclic presentation      285
Refinement of ordered partition      120
Regular action      18 23 62
Regular expression      435
Regular language      433 435
Regular normal subgroup, abelian      139
Regular normal subgroup, nonabelian      141
Reidemeister — Schreier algorithm      3 173 198 352 373
Rel(X)      413
1 2 3 4
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