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Dehn E. — Algebraic Equations
Dehn E. — Algebraic Equations

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Название: Algebraic Equations

Автор: Dehn E.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1930

Количество страниц: 208

Добавлена в каталог: 08.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel      110
Abelian equation      171 172
Abelian group      115 116 117 118 172
Absolute order      117
Abstract group      109 126
Abstract group, quotient      109
Adjunction      14 129 144 164 165 166 170
Affected equation      153
Algebra      1
Algebra, fundamental theorem of      10 184
Algebraic domain      181 132 133 135
Algebraic domain, degree of      131
Algebraic domain, function in      130 132
Algebraic domain, number in      130 133 135
Algebraic equation      1 184
Algebraic function      1
Algebraic operation      1 80 152 170 183
Algebraic root      184
Algebraic solution      1
Algorism, Euclid’s      4
Alternating function      15 54 55
Alternating group      56 57 58 61 125
Alternating group in 2 letters      58
Alternating group in 3 letters      58
Alternating group in 4 letters      58
Alternating group, composition-series of      61
Alternating group, normal subgroups of      61
Alternating group, subgroups of      62
Associative law      23 126
Binomial equation      76 78 193 195
Binomial equation, group of      195
Binomial resolvent      76 78
Biquadratic equation      75 90
Biquadratic equation, discriminant of      95
Biquadratic equation, solution of      75 97
Bring      196
Bring — Jerrard normal form of quintic      195 200
Cardan’s formula      11
Cauchy      17 27
Cauchy, theorem of      119
Cayley’s Theorem      127
Central subgroup      115 116
Circular group      82 102 173 174
Circular notation      18
Circular permutation      18 21 56 58 101 123
Circular permutation, diagram of      18
Circular permutation, order of      22
Class of permutations      118 119
Co-set      30
Combination, law of      19 126
Common factor      4 5 6 131
Common factor, greatest      4
Common root      47
Common subgroup, greatest      53 64 110
Commutative elements      127
Commutative group      115 127
Commutative law      20
Commutative permutations      20 21 23 24 37 115 119
Complete Galoisian function      143 144
Composite group      37 61
Composition, factors of      53
Composition, resolvent of      168 169 173
Composition-series      53 81 113 115 120 121
Composition-series of alternating group      61
Composition-series of symmetric group      61 120
Composition-series of transitive group      121
Composition-series, factor-group of      113 115
Composition-series, transitive      121
Congruence      178
Congruence group      121
Congruence, root of      178
Conjugate domains      133
Conjugate factors      166
Conjugate functions      30 34 66 80 101 139 150 151 154 155 156
Conjugate functions, permutations between      64
Conjugate numbers      133 134
Conjugate permutations      33
Conjugate subgroups      33 34 99 103 150 155
Conjugate values      see “Conjugate functions”
Conjugate values, sum of      73
Conjugate values, symmetric function of      72 73
Constancy of composition-factors      113
Construction of regular polygon      187 189
Continuity of functions      9
Cubic equation      11 52 75 79 83
Cubic equation, discriminant of      52
Cubic equation, solution of      11 13 89
Cycle of permutation      18 38 56
Cycle of roots      173 174
Cycle, degree of      19
Cycle, order of      21
Cycle, period of      21
Cyclic equation      172 173 174 183
Cyclic equation, roots of      174
Cyclic group      29 32 101 115 116 120 121 123 172 173
Cyclotomic equation      176 182 183 184 185
Cyclotomic equation, discriminant of      184
Cyclotomic equation, group of      182
Cyclotomic equation, roots of      189
Degree of algebraic domain      131
Degree of cycle      19
Degree of group      29
Degree of permutation      18 23 56
Degree of system      102
Degree, prime      23 32 173 190 191 192 193 195
Degree, total      45
Diagram of circular permutation      18
Diophantine equation      178
Direct product      108 118
Discriminant      50 51
Discriminant of biquadratic      95
Discriminant of cubic      52
Discriminant of cyclotomic      184
Discriminant of quadratic      51
Discriminant of quintic      199
Discriminant, root of      52 55 56
Division of functions      3
Division of groups      108
Division of permutations      25
Divisor of function      7
Domain      11 129
Domain of general equation      153
Domain of rational numbers      129 182 195
Domain, algebraic      131 132 133 135
Domain, imprimitive      136 162 163
Domain, invariant      136
Domain, normal      136 144 165
Domain, primitive      136 162
Domain, rational in      129
Domains, conjugate      133
Double (multiple) root      10 51 131 141 171 193
Doubly transitive group      104
Duality of plans      155
Durchschnitt      53
Eisenstein’s theorem      8
Element      126
Element, generating      127
Element, identical      127
Element, inverse of      127
Elementary Galoisian function      141 144
Elementary symmetric function      41 43
Elements, commutative      127
Elements, group of      127
Elements, multiplication table of      127
Elements, product of      127
Elimination      1
Equation of prime degree      173 190 191 192 193 195
Equation with affect      153
Equation without affect      153 154 155
Equation, Abelian      171 172
Equation, affected      153
Equation, algebraic      1 184
Equation, binomial      76 78 193 195
Equation, biquadratic      75 90
Equation, cubic      11 52 75 79 83
Equation, cyclic      172 173 174 183
Equation, cyclotomic      176 182 183 184 185
Equation, Diophantine      178
Equation, general      73 75 81 82 152 153 154 155 156
Equation, group of      145 (see also “Galoisian group”)
Equation, imprimitive      162
Equation, invariant      136
Equation, irreducible      131 134 135 136 158 171 172 182 190 191 192 193
Equation, irreducible but solvable      190 191 192 193
Equation, metacyclic      115 190 195
Equation, normal      136 144 158 169 171 173 182
Equation, quadratic      51 82
Equation, quintic      195 200
Equation, rational      131 148
Equation, reducible      157
Equation, resolvent      66 150 151 154 156 167 168 183
Equation, solution of      1 (see also “Equation solvable”)
Equation, solvable      80 152 170 183 191 192 193 195 200
Equation, special      139 149 152 155 156
Equation, unaffected      153 154 155
Euclid’s algorism      4
Euler      190
Even permutation      56 57 126
Extraction of root      1
Factor, common      4 5 6 131
Factor, greatest common      4
Factor, irreducible      6 156 157
Factor-group      110 111 115
Factor-group of composition-series      113 115
Factor-group, order of      110
Factors of composition      53
Factors, conjugate      166
Field      129
Finite group      126
FORM      195
FORMAT      179
Format, numbers      190
Format’s theorem      179
Formula of Cardan      11
Formula of Lagrange, interpolation      2 122
Function belonging to group      27 28 34 64 72 73 110 149 150
Function in algebraic domain      130 132
Function of Galois      140 141 142 143 144 146 149
Function, algebraic      1
Function, alternating      15 54 55
Function, complete Galoisian      143 144
Function, continuity of      9
Function, division of      3
Function, divisor of      7
Function, elementary Galoisian      141 144
Function, elementary symmetric      41 43
Function, Galoisian      140 141 142 143 144 146 149
Function, group on      64 65 101 167
Function, highest      41
Function, integral      1 2 10 132 142
Function, irreducible      6 8 130 131 134 143
Function, primary Galoisian      143 144 146 149
Function, primitive      7
Function, product of      7 10
Function, rational      1 2 67 129 131 132 142 143 146 147 148 149 150 151 154 155 156 164
Function, reducible      6 130
Function, root of      10
Function, symmetric      15 40 43 154
Functions, Conjugate      30 34 66 80 101 139 150 151 154 155 156
Fundamental theorem of algebra      10 184
Fundamental theorem of symmetric functions      43
Galois      1 11 36 119 140 155 156
Galois, plan of      140 149 152 155 166 168
Galois, theorem of      190
Galoisian function      140 141 142 143 144 146 149
Galoisian function, complete      143 144
Galoisian function, elementary      141 144
Galoisian function, primary      143 144 146 149
Galoisian group      145 146 147 148 149 151 152 154 155 156 166 169 170
Galoisian group, property (1) of      146
Galoisian group, property (2) of      148
Galoisian resolvent      143 144 145 149 151 166 167 169
Galoisian resolvent, conjugate factors of      166
Gauss      181 187
General equation      73 75 81 82 152 153 154 155 156
General equation, domain of      153
General equation, group of      154 155
General resolvent      193
Generalized theorem of Lagrange      151
Generating element      127
Generating permutation      38
Greatest common factor      4
Greatest common subgroup      53 64 110
Group      11 27 28 29 127 141
Group of binomial equation      195
Group of cyclotomic equation      182
Group of elements      127
Group of equation      145 (see also “Galoisian group”)
Group of general equation      154 155
Group of permutations      27 29 127
Group of prime degree      120 121 123 124 125
Group of prime degree and order      32 123
Group of prime order      32
Group of resolvent      67 167
Group of special equation      155
Group on functions      64 65 101 167
Group theory      27 126 127
Group, abelian      115 116 117 118 172
Group, abstract      109 126
Group, alternating      56 57 58 61 125
Group, circular      32 102 173 174
Group, commutative      115 127
Group, composite      37 61
Group, congruence      121
Group, cyclic      29 32 101 115 116 120 121 123 172 173
Group, degree of      29
Group, doubly transitive      104
Group, finite      126
Group, Galoisian      see “Galoisian group”
Group, half-metacyclic      125 126 198
Group, identity      29 32 37 115 120 121 141 143 144
Group, imprimitive      105 106 162
Group, index of      31 33
Group, intransitive      101 102 157
Group, linear      121
Group, metacyclic      115 121 123 124 125 126 190 198
Group, non-primitive      105
Group, order of      29 31 32 33 107 108 127
Group, partition of      30
Group, primitive      105 162
Group, quadratic      61
Group, reduction of      164 170
Group, regular      103 158 182
Group, simple      37 61
Group, simply transitive      104
Group, soluble      115 116 118 120 124 169 173
Group, symmetric      29 38 61 120 154 155 156
Group, transform of      33 99
Group, transitive      101 102 103 104 105 120 121 124 156 158 173 190
Groups, direct product of      108 118
Groups, division of      108
Groups, isomorphic      99 100 127
Groups, multiplication of      107
Groups, n to 1 isomorphic      100
Groups, product of      107
Groups, quotient of      109 110
Groups, simply isomorphic      99 146
Groups, theory of      27 126 127
Half-metacyclic group      125 126 198
Half-metacyclic in 5 letters      126
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