|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Dehn E. — Algebraic Equations |
|
|
|
| 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
|
|
|
| Реклама |
|
|
|
|
|
О проекте