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Magnus W., Karrass A., Solitar D. — Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations
Magnus W., Karrass A., Solitar D. — Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations

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Название: Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations

Авторы: Magnus W., Karrass A., Solitar D.

Аннотация:

This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2004

Количество страниц: 464

Добавлена в каталог: 10.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $A_{0}$      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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