Holt D.F., Bettina E., Eamonn O. — Handbook of Computational Group Theory :: Электронная библиотека попечительского совета мехмата МГУ

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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

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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

Предметный указатель

Cyclic extension method (for finding subgroups)      385
Cyclic group      12
Cyclic permutation (of a word)      36
Cyclically reduced word      36
Database, perfect groups      400
Database, primitive permutation groups      394
Database, small groups      402
Database, transitive permutation groups      397
Databases of groups      393
de la Harpe, P.      452 468
Deep — Thought      284
define      153
DefineSchreierGenerators      175
Defining relation      37
Defining relation of a monoid      415
Defining relator      37
Definition (in power-conjugate presentation)      358
Degree of group representation      49
Dehn algorithm      1
Dehn, M.      1 371
Dekimpe, K.      409
Depth (in polycyclic group)      277
DepthVector      223
Derivation      51
Derivation, principal      52
Derived series      28
Derived series, computing      73
Derived subgroup      28
DescendantSubgroups      192
Deterministic algorithm      67
Dfa (deterministic finite state automaton)      435
Diaconis, P.      144
Diameter of graph      147
Dietze, A.      188
Dihedral group      12
Direct product of groups      10
Direct product of groups internal      30
DISCRETA      392
Discrete log problem      220 272
Dixon, J.D.      3 255 257 260 394 396
Dobcsanyi, P.      198
Double coset      131
Double coset representatives computing      131 329
Driscoll, J.R.      147
Dunfield, N.M.      352
EARNS (elementary abelian regular normal subgroup)      139
EARNS (elementary abelian regular normal subgroup), computing      139
Easdown, D.      133 137
Eick, B.      2 6 274 295 301 311 320 364 371 374 384 394 396 402 403 409
Element(s), order of (computing)      66 72 269
Element(s), powers of (computing)      72
Element(s), random      69 95 136 218 272
Elementary abelian p-group      11
Eliminating generators (from group presentation)      41 185
Endomorphism      15
Endomorphism algebra of KG-module      50
Endomorphism algebra of KG-module, computing      237 241
Enveloping algebra      231
Epimorphism      15
Epimorphism, natural      16
Epimorphisms      330
Epstein, D.B.A.      433 469
Equivalent actions      17
Equivalent extensions      53
Equivalent representations      49
Erobenius automorphism      59
Error-correcting code      118 145 146
Essential rule in rewriting system      421 458
Euclidean group      452
Euler $\phi$ -function      17 59 391
Even, S.      147
ExistsWord      449
Exponent of a group      58
Exponent vector      276
Exponent-p class      355
Exponents, power      278
Extension      56 see
Extension, KG-module      52
F(2, 9)      373 468
F(2, n)      373
Factorization problem in permutation groups      148
Factorizing polynomials      226
Faithful action      18
Fellow-traveller property      454 468
Felsch method (coset enumeration)      165
Felsch, H.      165
Felsch, V.      2 3 170 311 317 373
Fibonacci group      160 373
Field, algebraic element      56
Field, characteristic of      57
Field, extension      56
Field, finite      57
Field, primitive element      59
Field, splitting      57
Field, transcendental element      56
Finite fields      57
Finite fields, computing in      220
Finite quotients, computing      326 352
Finite state automaton      422 433 434
Finite state automaton in rewriting systems      439
Finite state automaton, 2—variable      442
Finite state automaton, accessible      436
Finite state automaton, coaccessible      436
Finite state automaton, composite      450 465 466
Finite state automaton, counting the language of      438
Finite state automaton, deterministic      435
Finite state automaton, enumerating the language of      437 463 470
Finite state automaton, equivalent      434
Finite state automaton, existential quantification      448
Finite state automaton, language of      434
Finite state automaton, making deterministic      443
Finite state automaton, minimizing      444 459
Finite state automaton, operations on      442
Finite state automaton, standardization of      447 459
Finite state automaton, transition table      436
Finite state automaton, trim      436
Finkelstein, L.      95 104
First cohomology group      52
First cohomology group, computing      249 304
First isomorphism theorem      16
FirstInClass      194
Frattini extension      404
Frattini lemma      22
Frattini rank      359
Frattini subgroup      32 404
Free Abelian group      46
Free abelian group, free basis of      46
Free group      33 452
Free monoid      415
Frobenius group      139
FSA      see “Finite state automaton”
FSA-Count      438
FSA-Enumerate      437
Fun(X)      413
Furst, M.L.      93 147
G-congruence      23 83
Galois group, computing      399
Gap      5 17 120 122 131 132 170 185 189 220 221 255 268 326 353 364 373 374 380 383 393 394 397 409 456
Gaschutz, W.      404
Geek, M.      7
GeneralSearch      114
Generate-p — Groups      369
Generators      12 13
Generators, Schreier      42 173
Generators, standard      272
Genetic algorithms      148
Geometrically finite group      452
Gersten, S.M.      452
Ghys, E.      452 468
Gilman, R.H.      418

GL(d, K)      14 49
GL(d, q)      14
GL(n, Z)      336
Glasby, S.      271 311
GO(d, q)      14
Goldreich, O.      147
Golod — Shafarevich bound      373
GoodBasePoints      266
Graham, R.L.      144
Graph      118 145
Graph, arc-transitive      198
Griess, R.L.      4
Gromov, M.      452
Group      9
Group action      17
Group algebra      49
Group extension      38 48 307
Group extension, computing      307
Group extension, presentation of      38
Group extension, split      38 51
Group extension, split (testing for)      253
Group module      see “KG-module”
Group presentation      36
Group representation      48 49
Group representation, absolutely irreducible      50
Group representation, degree of      49
Group representation, equivalent      49
Group representation, irreducible      49
Group representation, simple      49
Group ring      49
Group, $\Omega$ -simple      26
Group, abelian      10
Group, almost simple      269 378
Group, alternating      14
Group, Artin      452
Group, asynchronously automatic      451
Group, automatic      411 433 451
Group, biautomatic      451
Group, black-box      65
Group, braid      452
Group, centre of      16
Group, characteristically simple      26
Group, classical      14
Group, commutative      10
Group, Coxeter      425 452
Group, crystallographic      289
Group, crystallographic (enumeration)      407
Group, cyclic      12
Group, dihedral      12
Group, direct product      10
Group, elementary abelian      11
Group, euclidean      452
Group, exponent of      58
Group, free      33 452
Group, free abelian      46
Group, geometrically finite      452
Group, growth function of      411 434 441
Group, hyperbolic      452
Group, Kleinian      470
Group, nilpotent      29
Group, perfect      28
Group, permutation      13
Group, polycyclic      29 273 353 425
Group, presentation of      38
Group, semidirect product      50
Group, simple      14
Group, SLP      64
Group, small cancellation      452
Group, socle of      31
Group, soluble, solvable      29
Group, space      290 407
Group, supersolvable      288
Group, surface      425
Group, symmetric      13
Group, von Dyck      425
Group, word-hyperbolic      452 468
Growth function of a group      411 434 441
GU(d, q)      14
H char G      26
Hadamard bound      349
Haken manifold      352
Hall $\pi$ -subgroup      320
Hall, Marshall      431
Hall, Philip      372
Hashing      443
Havas, G.      2 3 162 170 178 184 347—349 352 353 372
Hazelgrove, B.      2 4 149 162
Heath, L.S.      60
Heineken group      188 467
Heineken, H.      430
Hermiller, S.M.      425
Hermite normal form      337
Hermite normal form, computing      347
HermiteForm      338
Heydemann, M.-C.      148
Higman, G.      372
Hillman, J.      432
Hippe, L.      170
Hiss, G., VI      4 236
HLT+Lookahead (coset enumeration)      164
Holt, D.F.      6 7 122 132 133 230 255 271 325 326 334 349 353 371 380 384 385 400 425 432 433 469
Homomorphism(s)      15 51
Homomorphism(s) of modules, computing      241
Homomorphism(s), between permutation groups      107
Homomorphism(s), computing with      74
Homomorphism(s), crossed      51
Homomorphism(s), defining      74
Homomorphism(s), kernel of      15
Homomorphism(s), monoid      413
Homomorphism(s), on permutation groups      105
Homomorphism(s), verifying      74
Honing, B.      396
Hopcroft, J.E.      93 446
Howlett, R.B.      271 452
Hulpke, A.      131 148 326 333 334 384 385 397 400
Hurt, D.F.      469
Hyperbolic group      452
ImageKernel      76
Imprimitive action      23
Indecomposable KG-module testing for      242
Index automaton      440
Index of a subgroup      11
Induced action on a block system      106
Induced action on an orbit      105
Induced polycyclic sequence      291
Induced polycyclic series      291
InducedPolycyclicSequence      294
Inn(G)      15
Inner automorphism      15
Internal direct product      30
Intersection of subgroups computing      124 311
Intransitive action      22
Inverse of a matrix computing      223
InvertMatrix      224
Irreducible KG-module      49
Irreducible KG-module, finding all      246
Irreducible KG-module, testing for      230
Irreducible representation      49
Irreducible rewriting system      421
Irreducible rule in rewriting system      421
Irreducible string in rewriting system      418
Isaacs, I.M.      49
Isomorphic groups      15
Isomorphic groups, testing for      317 326 333 371
Isomorphic KG-modules      49
Isomorphic KG-modules, testing for      244
Isomorphism      15
Isomorphism problem      1 432
Isomorphism theorem(s) for groups      16
Isomorphism theorem(s) for monoids      414

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