Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Kurosh A.G. — Theory of Groups (vol 1)
Kurosh A.G. — Theory of Groups (vol 1)

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Theory of Groups (vol 1)

Автор: Kurosh A.G.

Аннотация:

Translated from the second Russian edition and with added notes by K.A. Hirsch. Teoriya Grupp by Kurosh was widely acclaimed, in its first edition, as the first modern text on the general theory of groups, with the major emphasis on infinite groups. The decade that followed brought about a remarkable growth and maturity in the theory of groups, so that this second edition, an English translation, represents a complete rewriting of the first edition. The book can be used as a beginning text, the only requirement being some mathematical maturity and a knowledge of the elements of transfinite numbers. Many new sections were added to this second edition, and many old ones were completely revised: The theory of abelian groups was significantly revised; many significant additions were made to the section on the theory of free groups and free products; an entire chapter is devoted to group extensions; and the deep changes in the theory of solvable and nilpotent groups — one of the large and rich branches of the theory of groups — are covered in this work. Each volume concludes with Editor's Notes and a Bibliography.


Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1960

Количество страниц: 288

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$p^{\infty}$, group of type      56
Abel, N.H.      30
Abelian group      30
Abelian group of finite rank      140
Abelian group of infinite rank      140
Abelian group, complete      163
Abelian group, completely decomposable      211
Abelian group, divisible      163
Abelian group, finitely generated      145
Abelian group, free      142
Abelian group, of type $p^{\infty}$      56
Abelian group, primary      137
Abelian group, reduced      164
Abelian group, separable      218
Additive group of integers      38
Additive notation      37
Automorphisms      85
Automorphisms, group of      87
Automorphisms, identity      85
Automorphisms, inner      86
Automorphisms, inner, group of      88
Automorphisms, operator      108
Automorphisms, outer      86
Baer, R.      8 35 67 103 158 167 168 198 205 211 212 216 217 218 220
Basic subgroup      181
Basis of abelian group      142 148
Bauer, M.      70
Birkhoff, G.      89 151
Bourbaki, N.      231
Burnside, W.      11
Cancellation      34
Cancellation in words      125
Cauchy, A.      11
Cayley, A.      44 45 132 133
Center      81
Center, group without      81
centralizer      84
Cernikov, S.N.      9 170
Chain, derived      102
Chain, lower central      103
Chain, normal, ascending      113
Chain, normal, descending      113
Characteristic      207
Class, of conjugate elements      80
Class, of conjugate subgroups      82
Class, of partition      28
Class, of residues      75
Closure      184
Commutator      99
Commutator of subsets      103
Commutator subgroup      101
Complete group      92
Complete group, abelian      163
Complex of elements      46
Component of direct decomposition      120
Composition factor      112
Composition length      112
Composition series      112
Consequences of defining relations      129
Correspondence, one-to-one      72
Coset, double      63
Coset, left      60
Coset, representative of      60
Coset, right      61
Decomposition of group, left      60
Decomposition of group, right      61
Decomposition, direct      117
Decomposition, direct, isomorphic      124
Decomposition, into cosets      71
Derived group      101
Derry, D.      158 221
Direct factor      118
Direct product      117
Direct product with prescribed subgroups      122
Direct product, cartesian      122
Direct product, complete      122
Direct product, restricted      122
Direct product, unrestricted      122
Direct sum      137
Direct, decomposition      117
Direct, isomorphic      124
Divisible abelian group      163
Double module      63
Element of finite order      36
Element, central      81
Element, divisible      163
Element, finite, height of      170
Element, generating      46
Element, infinite, height of      170
Element, invariant      81
Element, inverse      32
Element, inverse, left (right)      33
Element, normalizer      79
Element, null      24
Element, of infinite order      36
Element, rational      98
Element, unit      24
Element, unit, left (right)      33
Elements of equal type      95
Elements, conjugate      64
Elements, conjugate, class of      80
Elements, per mutable      31
Elementwise permutable      59
Embedding of group into group      43
Endomorphisms      85
Endomorphisms, addition      152
Endomorphisms, multiplication of      87
Endomorphisms, null      85
Endomorphisms, operator      108
Endomorphisms, subtraction of      152
Endomorphisms, summable      152
Everett, C.J.      161
Exchange theorem, Steinitz      139
Extension, of group by another      76
Extension, of isomorphism      168
Factor group      35 72
Factor of normal series      110
Factor set      29
Factor, direct      118
Factor, Ulm      187
Fitting, H.      153
Four-group, Klein's      71
Free generators      128
Free group      127
Free group, abelian      142
Free module      161
Frobenius, G.      11 148
Galois, E.      11 68
Gauss, C.F.      148
Generators      46
Generators, system of      48
Generators, system of, free      128
Genus      207
Gol'fand, Yu. A.      95
Golovin, O.N.      103
Graev, M.I.      122
Group      30
Group of automorphisms      87
Group of homomorphisms      55
Group of matrices      38
Group of operator automorphisms      109
Group of roots of unity      38
Group of rotations, of circle      38
Group of rotations, of cube      41
Group of transformations      40
Group of type $p^{\infty}$      56
Group table, Cayley's      132
Group with operator domain      104
Group without center      81
Group, abelian      30
Group, additive, of integers      37
Group, additive, of rationals      37
Group, alternating      39
Group, commutative      30
Group, commutator      101
Group, complete      92
Group, countable      57
Group, cyclic      46
Group, cyclic, finite      46
Group, cyclic, infinite      46
Group, decomposition of      58
Group, derived      101
Group, elementary      97
Group, extension      76
Group, finite      31
Group, finitely generated      50
Group, free      127
Group, hamiltonian      67
Group, indecomposable      122
Group, locally infinite      37
Group, metabelian      99
Group, mixed      37
Group, multiplicative, of rationals      38
Group, nilpotent of class 2      99
Group, periodic      37
Group, primary      137
Group, quasi-cyclic      56
Group, quaternion      67
Group, simple      68
Group, symmetric      39
Group, torsion-free      37
Groups, ascending sequence of      51
Groups, limit of sequence of, direct      55
Groups, limit of sequence of, inverse      227
Haimo, F.      228
Hall, P.      89 103
Hamilton, W.R.      67
Hausdorff, F.      13
Height of element      170
Height of element, finite      170
Height of element, infinite      170
Higman, G.      228
Hoelder, O.      11 92 95 112 116
Holomorph      90
Homomorphism theorem      155
Homomorphism theorem for operators      128
Homomorphisms      27
Homomorphisms, canonical      29
Homomorphisms, group of      155
Homomorphisms, natural      29
Homomorphisms, operator      107
Hopkins, C      88
Ideal      105
Image      27
Image, inverse      27
Image, inverse, complete      73
Indecomposable group      122
INDEX      61
Intersection of subgroups      45
Invariants of finitely generated abelian group      151
Isomorphism      25
Isomorphism of direct decompositions      124
Isomorphism of normal series      111
Isomorphism theorem      76
Isomorphism theorem for operator groups      108
Isomorphism, extension of      168
Isomorphism, type preserving      194
Join of subgroups      48
Jonsson, B.      221
Jordan, C      11 112 116
Kaloujnine, L.      186 221
Kaplansky, L      231
Kernel      73
Kiskina, Z.M.      156 158
Klein, R      71 230
KontoroviC, P.G.      220
Krull, W.      8
Kulikov, L.Ya.      8 167 168 171 173 174 179 180 181 182 186 189 198 199 202 205 214 216
KuroS, A.G.      181 221
Lagrange, J.L.      62 63 80
Layer      170
Lemma for operator groups      108
Lemma, Zassenhaus'      77
Length, of normal series      110
Length, of product      51
Length, of reduced word      125
Levi, F.W.      35 99 221
Limit of sequence of groups, direct      55
Limit of sequence of groups, inverse      227
Linearly dependent      138 140
Linearly independent      138 140
Lorenzen, P.      35
Lowest      170
Lyapin, E.S.      89 205 211
Mackey, G.      231
Mal'cev, A.I.      9 103 221
Mapping of set, into itself      23
Mapping of set, onto itself      40
Mapping, homomorphic      27
Mapping, induced      43
Mapping, inverse      87
Mapping, inverse, left (right)      87
Mapping, isomorphic      25
Mapping, single-valued      23
Matrices, group of      40
Miller, G.A.      11
Mills, W.H.      95
Misina, A.P.      205 217
Module, double      63
Module, free      161
Module, over ring      158
Monogenic subgroup      107
Neumann, B.H.      8
Noether, Emmy      12
normalizer      79
Operation, algebraic      21
Operation, associative      22
Operation, commutative      22
Operation, inverse      25
Operator      104
Operator automorphism      108
Operator domain      107
Operator endomorphism      108
Operator homomorphism      104
Order of group      31
Order, of element      35
Order, of element, in operator group      160
Overtype      207
p-adic integers, group of      155
Partition, regular      29
Perfect subgroup      194
Periodic group      37
Periodic part      137
Periodic subgroup, maximal      137
Permutation      21 228
Permutation, even      39
Permutation, identity      39
Permutation, inverse      39
Permutation, multiplication of      21
Permutation, odd      39
Poincare, H.      62 84
Pontryagin, L .S.      221
primary group      137
Product of endomorphisms      87
Product of homomorphisms      156
Product of subsets      58
Product of threads      55
Product, cartesian      122
Product, direct      117
Product, direct, complete      122
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте