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Rotman J.J. — An Introduction to the Theory of Groups
Rotman J.J. — An Introduction to the Theory of Groups



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Название: An Introduction to the Theory of Groups

Автор: Rotman J.J.

Аннотация:

Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions.The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange's theorem, the Noether isomorphism theorems, symmetric groups, G-sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem.The middle portion of the book uses the Jordan-Holder theorem to organize the discussion of extensions (automorphism groups, semidirect products, the Schur-Zassenhaus lemma, Schur multipliers) and simple groups (simplicity of projective unimodular groups and, after a return to G-sets, a construction of the sporadic Mathieu groups).


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 513

Добавлена в каталог: 09.12.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$p_i$-reduced word      415
$\Omega$-composition series      152
$\Omega$-group      151
$\Omega$-indecomposable      153
$\Omega$-map      151
$\Omega$-series      152
$\Omega$-simple group      152
$\pi$-subgroup      110
$\pi'$ -subgroup      110
$\sigma$-congruent      236
Aanderaa, S.      450
Abbati, P.      1 57 58
Abel, N.H.      1 97
Abelian group      13
ACC      145
action      55
Adding a handle      409
Adian — Rabin theorem      469
Adian, S.I.      136
adjacency      174
Adjoining roots      92
Adjoint transformation      242
Admissible subgroup      151
Affine group Aff(n, k)      264
Affine group of the plane      71
Affine hyperplane      265
Affine isomorphism      266
Affine line      265
Affine m-subspace      265
Affine map      70
Affine n-space      265
Affinity      264
Alperin — Kuo theorem      210
Alphabet of Turing machine      421
Alternating bilinear form      235
Alternating group, $A_n$      23
Alternating group, infinite a.g. $A_{\infty}$      51
Amalgam      401
Artin, E.      227: 347
Ascending central series      113
Ascending chain condition      145
Associated graph to directed graph      356
Associated semigroup to Turing machine      426
Associated vector space to affine space      265
Associativity      10
Associativity, generalized      11
Attaching a 2-cell along $\alpha$      398
Attaching map      398
Automorphism, field      93
Automorphism, graph      174
Automorphism, group      104 156
Automorphism, Steiner system      295
Automorphism, tower      163
Auxiliary table      352
Axiom of Choice      481
Baer theorem      320
Baer — Levi theorem      391
Baer, R.      111 327 334 350 383
Balanced group      365
Base, HNN extension      407 411
Base, wreath product      172
Basepoint      370
Basic move of Turing machine      421
Basic subgroup      326
Basis, free abelian group      312
Basis, free group      343
Basis, free semigroup      349
Basis, theorem      128 319 447
Bijection      480
Bilinear form      235
Bilinear form, alternating      235
Bilinear form, symmetric      235
Binary tetrahedral group      350
Block, G-set      256
Block, nontrivial      256
Block, Steiner system      293
Boone theorem      417
Boone — Higman theorem      466
Boone's lemma      431
Boone, W.W.      430 450
Both chain conditions      146
Boundary word      435
Bouquet of circles      377
Braid group      347
Brandis, A.      210
Britton's lemma      414
Britton, J.L.      430
Bruck — Ryser Theorem      294
Burnside Basis Theorem      124
Burnside lemma      58
Burnside normal complement theorem      196
Burnside problem      136
Burnside theorem      107 110
Cameron, P.l.      286
Cancellation law      5 15
Cardano, G.      90
Carmichael — Witt theorem      297
Carmichael, R.      35
Cassidy, P.I.      34
Cauchy theorem      102
Cauchy, A.L.      1 4
Cayley      34
Cayley graph      357
Cayley theorem      52
Center      44
CenterIess      45
Central extension      201
Central isomorphism      151
Central series      117
Centralizer element      44
Centralizer subgroup      112
Centralizes      112
Chain conditions      see ACC DCC or
Character group      205 340
Characteristic, abelian group of rank      1 332
Characteristic, field      218
Characteristic, subgroup      104
Characteristically simple      106
Chevalley groups      246
Chief series      152
Chinese remainder theorem for G-sets      260
Church's thesis      423
Circle group T      18
Circuit      371
Class equation      74
Class of nilpotency      115
Classical groups      239
Classification theorem of finite simple groups      246
Closed path      368
Coboundary      183
Cocycle      180
Cocycle, identity      180
Cohomology group, first      212
Cohomology group, second      183
Cole, F.N.      225 292
Collapse      354
Collapse, double      31
Collapse, enumeration      354
Collineation      274
Collins, D.l.      430
Coloring      60
Common system of representatives      25
Commutative diagram      183
Commutator      33
Commutator, identities      119
Commutator, subgroup      33
Commute      5
Companion matrix      138
Complement      167
Complete factorization      6
Complete group      158
Complete set of coset representatives = transversal      178
Complete wreath product      175
COMPLEX      366
Complex, components      369
Complex, connected      368
Complex, covering      377
Complex, dimension      367
Complex, edge      367
Complex, isomorphic      371
Complex, pointed      370
Complex, quotient      373
Complex, simply connected      372
Complex, tree      372
Complex, universal covering      383
Complex, vertices      366
Complex, wedge      399
Components of complex      369
Composition factors      101
Composition series      98
Computation of Turing machine      422
Congruence class      13
Congruence on semigroup      349
Congruent matrices      236
Congruent matrices, $\sigma$-      236
Conjugacy class      43
Conjugate elements      31 43
Conjugate elements, subgroups      44
Conjugation      18
Connected complex      368
Continuation      381
Contraction of Steiner system      294
Contravariant functor      336
Convex combination      70
Corner, A.L.S.      334
Correspondence theorem      38
Coset      4
Countable      484
Counting principle      294
Covariant functor      335
Cover group      208
Covering complex      377
Covering map      382
Coxeter, H.S.M.      351
Crossed homomorphism      211
Cubic formula      90
CYCLE      3
Cycle, index      60
Cycle, structure, same      46
Cyclic group      21
Cyclic permutation of word      434
Cyclic subgroup      21
Cyclic submodule      135
Cyclically reduced word      434
DATA      179
DCC      146
Decision process      418
Dedekind law      37
Degree, field extension      93
Degree, G-set      55
Degree, vertex in graph      358
Dehn, M.      430
Derivation      211
Derived series      104
Derived subgroup = commutator subgroup      33
Descartes, R.      90
Descending central series      113
Descending chain condition      146
Diagram      435
Diagram, commutative      183
Dickson, L.E.      232 246
Dicyclic group $DC_n$      351
Dihedral group $D_{2n}$      68
Dilatation      228
Dimension, affine space      265
Dimension, complex      367
Dimension, projective space      273
Dimension, simplex      366
Direct factor      126
Direct product, $K \times Q$      40
Direct product, infinite      308
Direct sum, infinite      308
Direct sum, matrices      138
Direct sum, modules      135
Direct summand      126 308
Directed graph      356
Directed polygon      433
Directed polygon, labeled directed polygon      433
Dirichlet, P.G.L.      200
Disjoint permutations      5
Disjoint subcomplexes      368
Divisible by n      309
Divisible group      207 320
Division algorithm      486
Double coset      31
Doubly transitive      250
Dual diagram      323
Dyadic rationals      331
EDGE      367
Eilenberg, S.      358
Eilenberg- Moore      54
Elementary abelian p-group      42
Elementary divisors, abelian group      132
Elementary divisors, matrix      141
Elementary moves on path      369
Elementary operation in semigroup      426
Elementary transvection $B_{ij}(\lambda)$      220
Empty word      344
End path      368
End path class      368
Endomorphism      144
Endomorphism, ring      334
Engel theorem      115
Enumerates      422
Equivalence, characteristics      332
Equivalence, class      477
Erlangen program      72
Euclid's lemma      490
Euler $\varphi$-function      27
Euler — Poincare characteristic      384
Evaluation map      341
Even permutation      8
Exact sequence      307
Exact sequence, short      307
EXPONENT      26
Exponent, minimal      202
Ext(Q, K)      186
Extension      154
Extension, central      201
Extensions      183
Extensions, forms      238
Extensions, G-invariant      257
Extensions, normal series      99
Extensions, relation      477
Extra-special group      124
Factor group = quotient group      32
Factor group = quotient group, normal series      97
Factor set      180
Faithful G-set      248
Feit — Thompson theorem      107
Fermat theorem      26
Feynmann, R.P.      84
Fiber      380
Field      93
Finite field GF(q)      28
Finite module      135
Finite order, module      135
Finitely generated group      314
Finitely generated group module      135
Finitely presented      400
1 2 3 4
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