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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
$(A^G)$      14
$Alt(\Omega)$      14
$Aut_K(M)$      49
$B^1(G, M)$      52 305
$B^2(G, M)$      53 307
$C1_G(g)$      20
$C_G(g)$      20
$C_G(H)$      21
$C_n$      15
$dep_X(g)$      277
$D_{2n}$      12
$End_{Kg}(M)$      50
$exp_X(g)$      276
$F_q$      58
$F_X$ (free group on X)      35
$F_X^{ab}$ (free abelian group on X)      46
$G \times H$      10
$G \times M$      50
$G^{[i]}$      29
$G^{[\infty]}$      29
$G_(\Delta )$      20
$G_\alpha$      19
$G_\Delta $      20
$H^1(G, M)$      52 305
$H^2(G, M)$      53 307 401
$H_g$      19
$led_X(g)$      277
$N_G(H)$      21
$O_p(G)$      132
$O_{\infty}(G)$      132
$Stab_G(\alpha)$      19
$Syl_p(G)$      21
$Sym(\Omega)$      13 413
$x^y$      28
$Z^1(G, M)$      51 305
$Z^2(G, M)$      53 307
$\alpha^G$      19
$\Omega$-composition series      27
$\Omega$-group      26
$\Omega$-invariant      27
$\Omega$-invariant series      27
$\Omega$-invariant subgroup      26
$\Omega$-simple group      26
$\omega_g$      19
(X|R)      36
1-coboundary      52
1—cocycle      51
2—coboundary      53
2—cocycle      53
A*      34
Aachen — Sydney “Group” system      5
Abelian group(s)      10
Abelian group(s), fundamental theorem      345
Abelian group(s), presentation      47
Abelian quotients, computing      335
Absolutely irreducible KG-module      50
Absolutely irreducible KG-module, testing for      237
Absolutely irreducible representation      50
AbsolutelyIrreducible      239
ACE3 (coset enumeration)      2 4 170
ACLIB      409
Action intransitive      22
Action of a group      17
Action, affine      305 313 314
Action, block under      23
Action, coset      18
Action, equivalent      17
Action, faithful      18
Action, imprimitive      23
Action, kernel of      18
Action, n-(fold) transitive      22
Action, orbits      19
Action, primitive      23
Action, right regular      18 62
Action, transitive      22
Adian, S.I.      1 371
Affine action      305 313 314
Affine permutation groups      395
AG-system      274
Algebraic element of field      56
Algebraic number field      288
Algorithm, deterministic      67
Algorithm, Las Vegas      68 272
Algorithm, Monte Carlo      68 142 272
Algorithm, polynomial-time      109
Algorithm, randomized      67
Algorithm, rewriting      63 75
Almost simple group      269 378
Alt(n)      15
Alternating group      14
Alternating group, testing for      81
Archer, C.      403
Artin group      452
Artin, E.      383
Aschbacher's theorem (matrix groups classification)      269 395
Aschbacher, M.      269 395
Assmus, E.F.      145
Asynchronously automatic group      451
Atkinson's algorithm (for primitivity testing)      83
Atkinson, M.D.      83
Aut(G)      15
Automatic group      411 433 451
Automatic structure      433 451
Automatic structure with uniqueness      451
Automatic structure, shortlex      451
Automatic structure, shortlex, computing      456
Automorphism      15
Automorphism group      15
Automorphism group inner, outer      15
Automorphism group of a group (computing)      317 326 333 384
Automorphism group of a p-group (computing)      371
Automorphism group of combinatorial structure      118
Automorphism inner, outer      15
B(2, 6)      431
B(d, n)      372
B1—GM      252
Babai, L.      65 69 272
Baby Monster      2
Bachem, A.      349
Backtrack search      108
Base      2 77 82 87 88 264
Base image      88
Base image, partial      113
Base, change of      102
Base, computing      90
BaseSwap      103
Basic orbit      88 265
Basic stabilizer      88
Baumslag, G.      6 7 354
Beals, R.      83 271 272 377
Beetham, M.      171
Bendix, P.B.      417
Berlekamp algorithm (for polynomial factorization)      227
Berlekamp, E.R.      227
Besche, H.U.      2 394 402 403
Biautomatic group      451
Black-box group      65 271 272 384
Block design      118 145
Block system      23
Block system, computing      82
Block system, computing induced action on      106
Block under an action      23
BlockImageKernel      107
BlockStabilizer      107
BlockVerify      216
Boone, W.W.      1 149
Braid group      452
Bratus, S.      271 384
Brauer character table      248
Brauer, R.      246
Bray, J.      410
Breuer, T.      409
Brink, B.      452
Brooksbank, P.A.      272
Brown, Harold      408
Bruckner, H.      364
BSGS      see “Base strong
BSGS in matrix groups      264
BSGS in solvable groups      98
Buchberger, B.      417
Burnside group      372 431
Burnside group, restricted      372
Burnside problem      372
Burnside problem, restricted      372
Burnside — Brauer theorem      246
Burnside — Dixon — Schneider algorithm      255
Burnside's Lemma      19
Burnside, W.      4 246 255 372 391
Butler, G., v      77 122 132 265 268 385 397
Cameron, P.J.      383
Cannon, James W.      433 452
Cannon, John J.      5 132 199 256 268 301 320 334 380 384—386
Cannonito, F.B.      6 354
Canonical polycyclic sequence      296
CanonicalPolycyclicSequence      297
Cantor, D.G.      227
Card shuffling      144
CAS      5 255
Cauchy — Probenius lemma      20 374 390
Cayley      5 122 189
Cayley graph      18 147 411 453
Cayley graph, diameter      147
Celler, F.      66 269 272 304 311
Central series      29
Central series, lower      29 355
Central series, lower exponent-p      355
Central series, upper      29
Centralizer of a subgroup      21
Centralizer of a subgroup, computing      122 313
Centralizer of an element      20
Centralizer of an element, computing      122
Centralizing algebra      50
Centralizing algebra, computing      237
Centre of a group      16
Centre of a group, computing      123
CGT, v      
Change of base      102
Character space      260
Character table, Brauer      248
Character table, computing      255
Character, linear      263
Characteristic of field      57
Characteristic polynomial of a matrix, computing      226
Characteristic subgroup      26
Characteristically simple group      26
CharacteristicPolynomial      227
Charney, R.      452
Chemical isomers      390
CHEVIE      7
Chief factors      27
Chief series      27
Chief series, computing      381
Class map      256
Class matrix      256
Class, exponent-p      355
Class, nilpotency      29
Class-breadth conjecture      3 317
Classical group      14
Classification of finite simple groups      3 26 132 377 383 394
Coclass of a p-group      374
Cohen, A.M., vi      
Cohomology group, first      52
Cohomology group, first (computing)      249 304
Cohomology group, second      53
Cohomology group, second (computing)      254 307
Coincidence      158
Coincidence (in coset enumeration)      83 156
Collected Word      282
Collection algorithm      280
Combinatorial structures, computing automorphism group      118
Combinatorial structures, constructing      145
Combinatorial structures, enumerating      390
Comm(g, h), xvi      27
Common substring replacement (in a group presentation)      40 185
Commutative group      10
Commutator      27
Commutator subgroup      28
Commutator subgroup, computing      73
Comp(G, M)      55
Compatible pair      55
Complement      38 51 304
Complement system      320
Complement system, computing      321
Complement, computing      304
Complete rewriting system      418
Composition factors      27
Composition factors of KG-module      50
Composition series      27
Composition series of KG-module      50
Composition series, computing      381
compress      167
Compression of coset table      167
Condensation      4 236
Conder, M.      198
Confluent polycyclic presentation      280
Confluent rewriting system      418
Congruence      23 156
Congruence, on a monoid      413
Conjugacy classes      20
Conjugacy classes, computing      316 384
Conjugacy problem      1 469
Conjugacy testing      316
Conjugate elements      20
Consistent polycyclic presentation      280 354 428
ConstantDegreeFactorization      230
Constructive recognition algorithm      271
ConstructiveMembershipTest      296
Conway polynomial      59 220
Conway, J.H.      373 409
Cooperman, G.      95 104
Cooperstein, B.      396
Coppersmith, D.      221
Core of a subgroup      19
Cormen, T.H., vi, xvi      
Coset      11
Coset action      18
Coset action, computing      126
Coset automatic structure      469
Coset enumeration      1 2 63 149
Coset enumeration, coincidence      83
Coset enumeration, coset table method      165
Coset enumeration, modified      178
Coset enumeration, relator-based method      162
Coset table      151
Coset table, compression      167
Coset table, modified      174
Coset table, standardization      167
Coset, double      131
Coset, left, right      11
CosetEnumerationC      166
CosetEnumerationR      164
Cox, B.      132 384 385
Coxeter group      425 452
Coxeter, H.S.M.      1 149
Critical pair      417 420
Crystallographic group      289
Crystallographic group, enumeration      407
Curtis, R.T.      409
Cycle-type      21
Cyclic conjugates      36
1 2 3 4
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