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| Magnus W., Karrass A., Solitar D. — Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations |
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| Предметный указатель |
A-module 154
Abelian 2
Adjunction problems 401
Alexander ideal 157
Alexander polynomial 158
Ascending chain condition 114
Associated primitive elements 166
Associative algebra, freely generated 299
Associative algebra, freely generated of rank r 299
Automorphic modular groups 179
Automorphism, elementary 131
Baker — Hausdorff formula 368
Basic ideal 302
Basic Lie element 323
Basis theorem for Lie elements 323
Basis theorem of P. Hall 343
Betti groups 393
Betti number 146
Birkhoff — Witt, theorem of 331
Bracket, arrangement 288
Bracket, product 318
Braid groups 26 172
Burnside groups 81
Burnside problem 379
Burnside restricted problem 380
Canonical form of an element 26
Cartesian subgroup 193 412
Cayley diagram 57
Characteristic subgroup 74
Class of nilpotency 349
Closed subgroup 418 441
Cohomology theory 393
Color group 57
Coloring of a graph 61
Coloring of a graph, regular 62
Commutation 288
Commutator relation 373
Commutator subgroup 73
Commutator, n-fold 293
Commutator-power product 343
Complete set of relators 7
Completely distinguished 115
Completely indecomposable 250
Components of a commutator 289
Conjugacy problem 24 400
Conjugacy theorem 261
Covering of a path 62
Critical groups 408
Curly bracket operator 361
Cyclic groups 2
Cyclically reduced 33 188 212
Deficiency of a monomial 320
Defining relations, set of 7
Defining relators 7
Defining relators of an A-module 154
Degree 299
Dehn, fundamental problems of 24
Derivable relators 6
Derivation in JG 394
Derived group 293
Descending from a word 126
Deviation 313
Dihedral groups 10
Distinguished subgroups 114
Divisible groups 402
Double coset representative system of an extended Schreier system 239
Dynkin — Specht — Wever, theorem of 362
Element defined by a word 5
Elementary automorphism 130 131
Elementary Nielsen transformation 125
Elementary Tietze transformation 50
Elimination of a generator from  319
Embedding problems 401
Empty word 4
Endomorphism 74
Engel element 377
Engel module 377
Equivalence of words 12
Exponent, of an Abelian group 78
Exponent, of B(e,r) 379
Exponent, sum 76
Extended Schreier system 234
Extended symmetric group 163
Extended word problem 273
Filtered algebra 390
Filtration 390
Finite presentation 7
Finite presentation of an A-module 153
Finitely based, variety 407
Finitely generated 7
Finitely presented 7
Finitely presented, module 153
Finitely related 7
Formal power series 302
Four-group of Klein 3
Frattini group 419
Free A-module 154
Free Abelian generators 145
Free Abelian group 77
Free associative algebra 299
Free automorphism 170
Free differential calculus 393
Free factor 113 180
Free group 19 26 33
Free isomorphism 170
Free Lie algebra 300
Free polynilpotent 417
Free product 180
Free product of cyclic groups 39
Free product with amalgamated subgroups 198 207
Free substitution 120 129
Freely equal 34
Freely generated associative algebra 299
Freely generated Lie algebra 300
Freely reduced word 33
Freiheitssatz 252
Friedrichs, theorem of 363
Fully invariant subgroup 74
Fully regular product 411
Generalized word problem 131
Generating elements 5
Generating symbols 5
Generator 2 5
Graded algebra 390
Graph 58
Graph of a group 57 61
Graph, isomorphism 59
Group diagram 57
Group ring 358
Gruppenbild 57
Grushko — Neumann, theorem of 191
Hall — Higman, theorem of 387
Hall, Marshall, theorem of 386
Hall, P., basis theorem of 343
Hausdorff differentiation 374
Homogeneous components 299 391
Homogeneous terms 299
Hopf, theorem of 393
Hopfian 109 111 415
Identity element of a group 1
Identity in a reduced free group 74
Indecomposable 195
Indecomposable, completely 250
Indecomposable, strongly 227
Indecomposable, variety 409
Initial segment of a word 90
Integrally independent 152
Invariant factors 157
Inverse of a word 5
Isolated segment of a word 123
| Isomorphic hereditary integral property, i.h.i. property 248
Isomorphism problem 24
Jacobi identity 300 358
Juxtaposed product of words 5
Kaloujnine, theorem of 392
Klein four-group 3
Knot polynomial 158
Kostrikin, theorem of 387
Kurosh rewriting process 230
Kurosh subgroup theorem 243
L-polynomial 154
Lattice transformation 168
Left half of a word 123
Length of a coset 93
Length of a polynilpotent group 417
Length of a word 4
Less than 1/k group 398
Level of a basic Lie element 324
Level transformation 163
Levi, theorem of 107 109
Lie algebra 300
Lie element 318
Lie invariant 356
Locally infinite 403
Lower central series 293
Lower central series of free groups 337
Major initial segment 123
Major terminal segment 123
Mapping class groups 175
Metabelian variety 406
Minimal right coset function 99
Minor initial segment 123
Minor terminal segment 123
Moebius function 329
Monotonic reduction process 397
Multiplication of equivalence classes 13
n-sequence 391
Natural isomorphism 410
Neutral representative function 229
Nielsen reduced 123
Nielsen transformation 130
Nielsen — Schreier, theorem of 95
Nilpotency, class of 349
Nilpotent 293 349
Nilpotent, product 411
Non-Hopfian 260
Normal subgroup generated by a set of elements 71
Order relation on words 26
Orientation of a graph, coloring and 61
p-group 248
Path 60
Path, connected 60
Path, empty 60
Path, end point of 60
Path, initial point of 60
Path, inverse of 60
Polycyclic 417 418
Polynilpotent 417
Power relation 373
Power subgroup 77
Pre-Abelian presentation 149
Presentation of a group 7 13
Presentation of a subgroup 86 227
Primitive element 108 121
Primitive element, associated 166
Product of group elements 1
Product of groups 410
Product of substitutions 130
Proper automorphism 176
Proper symplectic group 178
Property of a group 413
Pseudo-addition 337
Pseudo-multiplication 338
Q-divisible 343
Quaternion group 10
R-algebra 299
Rank, of B(e,r) 379
Rank, of free Abelian group 77
Rank, of free group 74
Rank, of Nielsen transformation 125 130
Rank, of reduced free group 74
Reduced form in a free product 183
Reduced form in a free product with amalgamation 206
Reduced free group 74
Reduced sequence 181
Regular extended Schreier system 239
Regular product 411
Reidemeister rewriting process 91
Reidemeister rewriting process, theorem of 91
Reidemeister — Schreier rewriting process 93
Relation 6
Relation, matrix 146
Relation, module 354
Relator 6
Representative length in a free product with amalgamations 206
Representative of an equivalence class 13
Residual property 414
Residually finite 116 414
Residually nilpotent 349
Restricted Burnside problem 380
retract 81 139 248
Retractive homomorphism 81
Rewriting process 86 91 93 230
Right coset representative function 88
Right half of a word 123
Root 402
Root, property 416
Sanov, theorem of 384
Schreier right coset function 93
Schreier system 93
Schreier system, extended 234
Schreier system, extended, regular 239
Schreier system, minimal 93
Schreier theorem of 94
Simple commutator 79 293
Simple n-fold commutator 293
Simple product in a Lie algebra 342 359 361
Singular graph 59
Sirsov — Witt, theorem of 331
Soluble product 412
solvable 293
Standard basic Lie elements 334
Standard ordering of basic Lie elements 334
Stem of an L-polynomial 156
Strongly indecomposable 227
Subgroup topology 388
Substitution on generators, in a word 129
Substitution on generators, in a word in formal power series 309
Syllable 182
Syllable, length 79 182
Symmetric group, extended 163
Symmetric set of relators 398
Symplectic group 178 356
Symplectic group, proper 178
T-transformation 166
Takahasi, theorem of 108 249
Taylor theorem 375
Taylor theorem in JF 395
Tensor product 363
Terminal segment of a word 123
Tietze transformation 50
Titled exponent sum matrix 141
Torsion free 373
Torsion number 146
Total x-length 126
Transformation problem 24
Trivial relators 6
Unimodular group 39
Unit element of a group 1
Value of a formal power series 309
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