Rotman J.J. — An Introduction to the Theory of Groups :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

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Предметный указатель

Finitely related = finitely presented      400
First cohomology group      212
First isomorphism theorem      35
Fitting subgroup      118
Fitting's lemma, groups      147
Fitting's lemma, Q-groups      153
Fixed element of G-set      248
fixes      3
Four group = 4-group V      15
Frattini argument      81
Frattini subgroup $\Phi(G)$       122
Frattini theorem      123
Free Abelian group      312
Free group      343
Free product      388
Free product with amalgamated subgroup = amalgam      401
Free semigroup      349
Freely reduced word      434
Freiheitsatz      449
Fridman, A.A.      450
Frobenius complement      254
Frobenius group      254
Frobenius kernel      252
Frobenius, G.      58 132 199
Fuchs, L.      334
Full subcomplex      367
Fully invariant subgroup      108
Function      479
Functor, contravariant      336
Functor, covariant      335
Functor, left exact      336
Fundamental group      370
Fundamental Theorem Arithmetic      101 490
Fundamental Theorem Combinatorial Group Theory      436
Fundamental Theorem Finite Abelian Groups      132
Fundamental Theorem Finitely Generated Abelian Groups      319
Fundamental Theorem Finitely Generated Modules      142
Fundamental Theorem Projective Geometry      277
G-invariant equivalence relation      257
G-isomorphism      260
G-map      260
G-set      55
G-set, block      256
G-set, doubly transitive      250
G-set, faithful      248
G-set, imprimitive      256
G-set, isomorphism      282
G-set, k-transitive      250
G-set, multiply transitive      250
G-set, primitive      256
G-set, rank      249
G-set, regular      252
G-set, right      55
G-set, sharply k-transitive      251
G-set, trivial      248
Galois field GF(q)      218
Galois group      93
Galois theorem      96
Galois, E.      1 493
Gaschiitz theorem      191
Gaschiitz, W.      123
GCD      487
General linear group GL(n, k)      13 219
Generalized associativity      11
Generalized quaternions       87
Generates      22
Generators and relations, abelian groups      314
Generators and relations, groups      345
Godel image of presentation      465
Godel number      423
Graph      174
Graph, directed      356
Green, l.A.      366
Group      12
Group of motions $M(n, \mathbb{R})$       64
Group of units      13
Group, $M_{10}$       284
Group, $M_{11}$       288
Group, $M_{12}$       289
Group, $M_{22}$       290
Group, $M_{23}$       291
Group, $M_{24}$       292
Group, abelian      13
Group, affine Aff(n, k)      264
Group, affme group of the plane      71
Group, alternating       23
Group, automorphism group      156
Group, balanced      365
Group, binary tetrahedral      350
Group, braid      347
Group, characteristically simple      106
Group, circle $\mathbb{T}$       18
Group, classical      239
Group, complete      158
Group, cyclic      21
Group, dicyclic       351
Group, dihedral D      2n 68
Group, divisible      320
Group, elementary abelian p-      42
Group, extra-special      124
Group, finitely generated      314
Group, finitely related      400
Group, four group = 4-group V      15
Group, free      343
Group, free abelian      312
Group, fundamental      370
Group, Galois      93
Group, general linear GL(n, k)      13
Group, generalized quaternions       87
Group, hamiltonian      87
Group, holomorph      164
Group, icosahedral      69
Group, indecomposable      145
Group, infinite alternating $A_{\infty}$       51
Group, infinite dihedral $D_{\infty}$       391
Group, integers mod $n\mathbb{Z}_n$       13
Group, modular $PSL(2, \mathbb{Z})$       391
Group, nilpotent      115
Group, octahedral      69
Group, operator      151
Group, orthogonal $O(n, \mathbb{R})$       64
Group, orthogonal O(n, k)      239
Group, p-group      73
Group, p-primary      126
Group, perfect      263 358
Group, periodic      155
Group, projective unimodular PSL(n, k)      223
Group, quaternions Q      83
Group, quotient      32
Group, reduced abelian      322
Group, rotation      65
Group, simple      39
Group, solvable      97
Group, special linear SL(n, k)      23
Group, supersolvable      107
Group, symmetric       12
Group, symmetry group of figure      67
Group, symplectic Sp(2m, k)      238
Group, T (order      12) 84
Group, tetrahedral      69
Group, torsion      308
Group, torsion-free      155 308
Group, unitary U(n, k)      238
Group, unitriangular UT(n, k)      82
Groupoid      370
Gruen, O.      199
Gruenberg lemma      214
Gruenberg — Wehrfritz      215
Grushko theorem      393
h-special word      427

Hall subgroup      110
Hall theorem      108 110
Hall — Higman theorem      136
Hall, M.      387
Hall, P.      25 116 166
Hamilton, W.R.      69
Hamiltonian group      87
Height      332
Height, sequence      332
Hermitian form      235
Higher centers , $\zeta^i(G)$       113
Higher commutator subgroups $G^{(i)}$       104
Higman theorem      451
Higman, G.      86 136 407
Higman, Neumann, and Neumann theorem      404 405
Hirshon R.      150
HNN extension      407 411
Hoelder theorem      160 197
Hoelder, O.      101 154
Holomorph      164
Homogeneous coordinates      273
Homomorphism      16
Homomorphism, crossed      211
Homotopic      369
Hopf's formula      358
Humphreys, J.E.      391
Hyperbolic plane      240
Hyperplane      66 228
Icosahedral group      69
Idempotent endomorphism      144
Identity element      14
Identity function       480
Image = im      22
Imbedding      23
Imbedding free product      388
Imprimitive G-set      256
Imprimitive system      257
Inclusion function      480
Indecomposable group      145
Independence in abelian group      127 310
INDEX      25
Infinite alternating group $A_{\infty}$       51
Infinite dihedral group $D_{\infty}$       391
Injection      480
Injective property      320
Inner automorphism      156
Inner automorphism group Inn(G)      156
Inner product, matrix      235
Inner product, space      235
Instantaneous description      421
Instantaneous description, terminal      422
Integers mod $n\mathbb{Z}_n$       13
Intersection of subcomplexes      368
Invariant factors, abelian group      129
Invariant factors, matrix      139
Invariant subspace      135
Inverse element      14
Inverse function      480
Inverse image of subcomplex      377
Inverse word      344
Involution      68
Involves      413
Isometry      237
Isomorphism, complexes      371
Isomorphism, field      93
Isomorphism, G-sets      282
Isomorphism, groups      16
Ivanov, S.      136
Iwasawa criterion      263
Jacobi identity      118
James, R.      86
Johnson, D.L.      350
Jonsson, R      334
Jordan — Dickson theorem      232
Jordan — Hoelder theorem, $\Omega$ -groups      152
Jordan — Hoelder theorem, groups      100
Jordan — Moore theorem      225
Jordan, C.      101 286 289
Jordan, C., block      139
Jordan, C., canonical form      141
Jordan, C., decompositions      144
Juxtaposition      344
k-transitive      250
Kaloujnine, L.      176 187
Kaplansky, I.      19 330
Kernel, derivation      213
Kernel, group homomorphism      22
Kernel, ring homomorphism      485
Kernel, semigroup homomorphism      350
Klein, F.      72
Kostrikin, A.L.      136
Kronecker, L.      128
Kronecker, L., delta $\delta_{ij}$       498
Krull — Schmidt theorem, $\Omega$ -groups      153
Krull — Schmidt theorem, groups      149
Kulikov theorem      327
Kulikov, L.J.      330
Kurosh theorem      392
Kuznetsov, A.V.      466
Labeled directed polygon      433
Lagrange's theorem      26
Lagrange, J.-L.      1 57
Lam — Leep      162 285
Lam, C.      294
Landau, E.      77
Latin square      18
Least criminal      111
Left exact functor      336
Length, cycle      3
Length, normal series      97
Length, path      368
Length, word      418
Levi, F.      383
Lifting extension      178
Lifting path      378
Linear fractional transformation      281
Linear functional      229
Lodovici Ferrari      90
Lower central series      113
Lyndon, R.C.      433
Mac Lane, S.      358
Magnus, W.      449
Mann, A.      74
Mann, H.B.      31
Markov property      468
Markov — Post Theorem      428
Mathieu groups, $M_{10}$       284
Mathieu groups, $M_{11}$       288
Mathieu groups, $M_{12}$       289
Mathieu groups, $M_{22}$       290
Mathieu groups, $M_{23}$       291
Mathieu groups, $M_{24}$       292
Matrix of linear transformation, relative to ordered basis      137
Maximal divisible subgroup      321
Maximal normal subgroup      39
Maximal tree      373
McCormick, G.      200
McIver, A.      86
McKay, J.H.      74.
McLain, D.H.      115 176
Miller, C.F., III      430 467
Miller, G.A.      292
Minimal exponent      202
Minimal generating set      124
Minimal normal subgroup      105
Minimum polynomial      139
Modular group $PSL(2, \mathbb{Z})$       391
Modular law      37
Module      134
Monomial matrix      46 177

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