Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Burnside W. — Theory of Groups of Finite Order Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Theory of Groups of Finite Order Автор: Burnside W. Аннотация: A classic introduction to group theory for nearly a century, this is the book most often cited in texts on group theory for detailed expositions of basic concepts. After introducing permutation notation and defining group, the author discusses the simpler properties of group that are independent of their modes of representation; composition-series of groups; isomorphism of a group with itself; Abelian groups; groups whose orders are the powers of primes; and Sylow's theorem. Permutation groups and groups of linear substitutions receive an extensive treatment; two chapters are devoted to the graphical representation of groups, and the closing chapter to congruence groups. Forty-five pages of notes at the back of the book offer ample treatment of special topics. Язык: Рубрика: Математика/Алгебра/Теория групп/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1897 Количество страниц: 388 Добавлена в каталог: 26.03.2005 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель
 Abel, quoted      46 Abelian group of order and type (1, 1, ..., 1)      58 Abelian group of order and type (1, 1, ..., 1), group of isomorphisms of      243 244 Abelian group of order and type (1, 1, ..., 1), holomorph of      245 Abelian group of order and type (1, 1, ..., 1), number of distinct ways of choosing a set of independent generating operations of      59 Abelian group of order and type (1, 1, ..., 1), number of sub-groups of, whose order is given      60 Abelian group, definition of      46 Abelian group, definition of, existence of independent generating operations of      52 Abelian group, definition of, invariance of the orders of a set of independent generating operations of      54 Abelian group, definition of, sub-groups of      47 48 55—59 Abelian group, definition of, symbol for, of given type      55 Alternating group, definition of      139 Alternating group, definition of, group of isomorphisms of      246 Alternating group, definition of, is simple, except for degree 4      154 Bochert, quoted      153 Bolza, quoted      162 Burnside, quoted      65 97 157 311 317 335 345 352 365 370 Caucht, quoted      90 Cayley, quoted      306 Characteristic series, definition of      232 Characteristic series, definition of, invariance of      233 Characteristic series, definition of, of a group whose order is a power of a prime      233—235 Characteristic sub-group, definition of      232 Characteristic sub-group, groups with no, are either simple or the direct product of simply isomorphic simple groups      232 Chief composition series, or Chief series, definition of      123 Chief composition series, or Chief series, invariance of      123 Cole and Glover, quoted      137 Cole, quoted      196 370 Colour-groups      306—310 Colour-groups, examples of      310 Complete group, definition of      236 Complete group, group of isomorphisms of a simple group of composite order is a      238 Complete group, groups which contain a, self-conjugately are direct products      236 Complete group, holomorph of a cyclical group of odd order is a      241 Complete group, holomorph of an Abelian group of order and type (1, 1, ..., 1) is a      239 Complete group, symmetric group is a, except for degree 6      246 Composite groups, definition of      29 Composite groups, definition of, non-soluble      376—378 Composite groups, definition of, of even order      360—365 Composition factors, definition of      118 Composition-series, definition of      118 Composition-series, examples of      128 129 Composition-series, invariance of      122 Conjugate operations, definition of      27 Conjugate operations, definition of, complete set of      31 Conjugate sub-groups, complete set of      32 Conjugate sub-groups, definition of      29 Conjugate sub-groups, operations common to or permutable with a complete set of, form a self-conjugate sub-group      33 Dedekind, quoted      89 Defining relations for groups of genus unity      301 302 Defining relations for groups of genus zero      291 Defining relations for groups of order 133—137 Defining relations for groups of order pq      100 Defining relations for groups of orders , , 87 88 89 Defining relations for groups whose orders contain no square factor      354 Defining relations for the holomorph of a cyclical group      240 241 Defining relations for the simple group of order 168      305 Defining relations for the symmetric group of degree 5      305 Defining relations of a group, definition of      21 Defining relations, limitation on the number of, when the genus is given      283 Degbee of a substitution group, definition of      138. Degbee of a substitution group, is a factor of the order, if the group is transitive      140 Direct product of two groups, definition of      40 Direct product of two groups, represented as a transitive group      190 Direct product of two simply isomorphic groups of order n represented as a transitive group of degree n      146 147. Doubly transitive groups, generally contain simple self-conjugate sub-groups      192 Doubly transitive groups, of degree n and order n(n-1)      155—157 Doubly transitive groups, the sub-groups of, which keep two symbols fixed      212 Doubly transitive groups, with a complete set of triplets      214 Dtcck, quoted      22 44 172 195 255 292 301 305 Dyck’s theorem that a group of order n can be represented as a regular substitution group of degree n      22—24 Factor groups, definition of      38 Factor groups, invariance of      118. Factor groups, set of, for a given group      118 Forsyth, quoted      280 283 Fractional linear group, analysis of      319—333 Fractional linear group, definition of      311 Fractional linear group, generalization of      334 335 Frobenius and Stickelberger, quoted      46 Frobenius, quoted      39 45 65 71 90 97 108 110 114 166 232 250 251 345 354 358 360 Frobenius’s theorem that, if n is a factor of the order of a group, the number of operations of the group whose orders divide n is a multiple of n      110—112 Galois, quoted      192 334 General discontinuous group with a finite number of generating operations      256 General discontinuous group, relation of special groups to      257 258 Genus of a group, definition of      280 Gierster, quoted      311 Graphical representation, of a cyclical group      260 261 288 Graphical representation, of a general group      262—266 Graphical representation, of a group of finite order      273—278 Graphical representation, of a group of finite order, examples of      269—272 279 288—290 294 296 299 300 303 310 Graphical representation, of a special group      266—269 Group of isomorphisms, contains the group of cogredient isomorphisms self-con jugately      226 Group of isomorphisms, of a cyclical group      239—242 Group of isomorphisms, of an Abelian group of order and type (1, 1, ..., 1)      243 244 311—317 336—338 Group of isomorphisms, of doubly transitive groups of degree and order 246—248 Group of isomorphisms, of the alternating group      246 Group, abelian      46 Group, alternating      139 Group, complete      236 Group, continuous, discontinuous, or mixed      13 14 Group, cyclical      25 Group, defining relations of      21 Group, definition of      11 12 Group, dihedral      287 Group, fundamental or generating operations of      21 Group, general      256 Group, genus of a      280 Group, group of isomorphisms of a      223 Group, holomorph of a      228 Group, icosahedral      289 Group, multiplication table of      20 49 Group, octohedral      289 Group, order of      14 Group, quadratic      326 Group, simple and composite      29 Group, soluble      130 . Group, special      257 Group, symbol for a      27 (see also “Substitution group”) Group, symmetric      139 Group, tetrahedral      289 . Groups of genus one      295—302 Groups of genus two      302 Groups of genus zero      286—292 Groups whose order is , where p is a prime      61 et seq. Groups whose order is always contain self-conjugate operations      62 Groups whose order is case in which there is only one sub-group of a given order      72—75 Groups whose order is determination of distinct types of orders , , , where p is an odd prime      81—88 Groups whose order is every sub-group of, is contained self-conjugately in a greater sub-group      65 Groups whose order is number of sub-groups of given order is congruent to unity, mod. p      71 Groups whose order is number of types which contain self-conjugate cyclical sub-groups of order 76—81 Groups whose order is table of distinct types of orders 8 and 16      88 89 Groups whose orders contain, no cubed factor      359 Groups whose orders contain, no squared factor      353 354 Groups whose sub-groups of order are all cyclical      352 353 Heffter, quoted      215 Holder, quoted      38 87 119 137 224 236 246 249 344 353 370 376 Holomorph of a cyclical group      240—242 Holomorph of an Abelian group of order and type (1, 1, ... 1)      245 Holomorph, definition of      228 Homogeneous linear group, composition series of      314—317 Homogeneous linear group, definition of      244 Homogeneous linear group, generalization of      340—342 Homogeneous linear group, represented as a transitive substitution group      336 337 Homogeneous linear group, simple groups denned by      338 339 Hukwitz, quoted      24 280 282 Identical opebation, definition of      12 Imprimitive groups of degree 6      181 182 Imprimitive groups, definition of      171 Imprimitive self-conjugate sub-group of a doubly transitive group      193 194 Imprimitive systems of a regular group      173 Imprimitive systems of any transitive group      176 Imprimitive systems, definition of      172 Imprimitive systems, properties of      185 186 Intbansitive groups, definition of      140 Intbansitive groups, of degree 7 with transitive sets of 3 and 4      163 164 Intbansitive groups, properties of      159—162 Intbansitive groups, transitive sets of symbols in      159 166 Isomoephism of general and special groups      257 258 Isomoephism of two groups, general, definition of      41 Isomoephism of two groups, multiple, definition of      36 Isomoephism of two groups, simple, definition of      32 Isomoephisms of a group with itself, definition of      222 Isomoephisms of a group, class of, definition of      224 Isomoephisms of a group, cogredient and contragredient, definition of      224 Isomoephisms of a group, limitation on the order of      252 Joedan, quoted      46 119 143 146 149 150 153 189 196 198 204 311 Klein and Feicke, quoted      162 Klein, quoted      224 289 292 Limitation on the number of defining relations of a group of given genus      283 Limitation on the order of a group of given genus      282 Maeggeaff, quoted      198 Maillet, quoted      108 Maschke, quoted      310 Mathieu, quoted      155 Maximum self-conjugate sub-group, definition of      35 Maximum sub-group, definition of      35 Millee, quoted      105 196 259 Minimum self-conjugate sub-group is a simple group or the direct product of simply isomorphic simple groups      127 Minimum self-conjugate sub-group, definition of      124 Mooee, quoted      215 335 Multiplication table of a group      20 49 Multiply isomoephic groups, definition of      36 Netto, quoted      141 198 215 Numbee of symbols unchanged by all the substitutions of a group      165 166 Operations common to two groups form a group      27 Operations of a group, which are permutable with a given operation or sub-group, form a group      29 31 Operations, common to or permutable with each of a complete set of conjugate subgroups form a self-conjugate sub-group      33 Order of a group, definition of      14 Order of an operation, definition of      14 Permutability of an operation with a group, definition of      29 Permutable groups, definition of      41 Permutable opeeations, definition of      12 Primitive groups, definition of      171 Primitive groups, limit to the order of, for a given degree      199 Primitive groups, of degree 6      205 206 Primitive groups, of degree 7      206—208 Primitive groups, of degree 8      209—211 Primitive groups, of degrees 3, 4 and 5      205 Primitive groups, of prime degree      201 Primitive groups, when soluble, have a power of a prime for degree      192 Primitive groups, with a transitive sub-group of smaller degree      197 198 Primitivity, test of      184 Regular division of a surface, representation of a group by means of      278 Repeesentation, graphical      see “Graphical representation” Representation of a group, in primitive form      177 Representation of a group, in transitive form. i.e. as a transitive substitution group      22 173—179 Self-conjugate operation, definition of      28 Self-conjugate operation, of a group whose order is the power of a prime      62 Self-conjugate operation, of a transitive substitution group must be a regular substitution      144 Self-conjugate sub-group, definition of      29 Self-conjugate sub-group, generated by a complete set of conjugate operations      34 Self-conjugate sub-group, of a k-ply transitive group is, in general, (k-1)-ply transitive      189 Self-conjugate sub-group, of a primitive group must be transitive      187 Self-conjugate sub-group, of an imprimitive group      187 188 Simple groups, definition of      29 Simple groups, whose orders are the products of not more than 5 primes      367—370 Simple groups, whose orders do not exceed 660      370—375 Simply isomorphic groups, definition of      22 Simply isomorphic groups, said to be of the same type      22 Soluble groups, definition of      130 Soluble groups, properties of      131 132 Soluble groups, special classes of      345—359 Sub-group, definition of      25 Sub-group, order of a, divides order of group      26 (see also “Conjugate” “Self-conjugate” Substitution group, conjugate substitutions of, are similar      144 Substitution group, construction of multiply transitive      150 Substitution group, degree of transitive, is a factor of its order      140 Substitution group, degree of, definition of      138 Substitution group, doubly transitive, of degree n and order n(n-l)      155—157 Substitution group, limit to the degree of transitivity of      152 Substitution group, multiply transitive, definition of      148 Substitution group, order of a ft-ply transitive, whose degree is n, is a multiple of n(n-1)...(n-k+1)      148 Substitution group, primitive and imprimitive, definition of      171 Substitution group, quintuply transitive, of degree 12      170 Substitution group, regular, definition of      24 Substitution group, representation of any group as a regular      22 Substitution group, transitive and intransitive, definition of      140 Substitution group, transitive, whose substitutions, except identity, displace all or all but one of the symbols      141—144 Substitution group, triply transitive, of degree n and order n(n-l)(n-2)      158 Substitution groups whose orders are powers of primes      218 219 Substitution, circular      7 Substitution, cycles of      2 Substitution, definition of      1 Substitution, even and odd      10 Substitution, identical      4 Substitution, inverse      4 Substitution, order of      6 Substitution, permutable      8 Substitution, regular      7 Substitution, similar      7 Substitution, symbol for the product of two or more      4 Substitutions which are permutable, with a given substitution      215 216 Substitutions with every substitution of a given group      145 146 217 Substitutions with every substitution of a group, whose degree is equal to its order, form a simply isomorphic group      146 Sylow, quoted      62 90 Sylow’s Theorem      92—95 Sylow’s theorem, extension of      110 Sylow’s theorem, some direct consequences of      97—100 Symbol for a group generated by given operations      27 Symbol for the product of two or more operations      12 Symbol for the product of two or more substitutions      4 Symbol, and , definition of      250 251 Symmetric group, definition of      139 Symmetric group, is a complete group, except for degree 6      246 Symmetric group, of degree 6 has 12 simply isomorphic sub-groups of order 5! which form two distinct conjugate sets      200 Symmetric group, of degree n has a single set of conjugate sub-groups of order (n-1)! except when n is 6      200 Transforming an operation, definition of      27 Transitive group, definition of      140 Transitive group, number of distinct modes of representing the alternating group of degree 5 as a      179 180 Transitive group, representation of any group as a      175—179 Transpositions, definition of      9 Transpositions, number of, which enter in the representation of a substitution is either always even or always odd      10 Transpositions, representation of a substitution by means of      9 Triply transitive groups of degree n and order n(n-l)(n-2)      158 type of a group      see “Simply isomorphic groups” Types of group      8 or 16 88 89 Types of group 24      101—104 Types of group 60      105—108 Types of group, , where p and q are different primes      133—137 Types of group, distinct, whose order is , , or , where p is an odd prime      87 88 Types of group, pq, where p and q are different primes      100 101 Weber, quoted      46 Young, quoted      63 68 87 310 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2022 | | О проекте