The theory of substitutions and its applications to algebra:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Bronx, NY
Chelsea
1964
|
| Edition: | 2. ed., rev. by the author |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 304 S. |
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MARC
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| 240 | 1 | 0 | |a Substitutionentheorie und ihre Anwendungen auf die Algebra |
| 245 | 1 | 0 | |a The theory of substitutions and its applications to algebra |
| 250 | |a 2. ed., rev. by the author | ||
| 264 | 1 | |a Bronx, NY |b Chelsea |c 1964 | |
| 300 | |a XI, 304 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Equations, Theory of | |
| 650 | 4 | |a Group theory | |
| 650 | 0 | 7 | |a Substitution |0 (DE-588)4183925-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804118057959817216 |
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| adam_text | TABLE OF CONTENTS.
PART I.
Theory op Substitutions and of Integral Functions.
CHAPTER I.
SYMMETRIC OR SINGLE VALUED FUNCTIONS ALTERNATING AND TWO VAL¬
UED FUNCTIONS.
1 3. Symmetric and single valued functions. 1.
4. Elementary symmetric functions.
5 10. Treatment of the symmetric functions.
11. Discriminants.
12. Euler s formula.
13. Two valued functions; substitutions.
14. Decomposition of substitutions into transpositions.
15. Alternating functions.
16 20. Treatment and group of the two valued functions.
CHAPTER II.
MULTIPLE VALUED FUNCTIONS AND GROUPS OF SUBSTITUTIONS.
22. Notation for substitutions. 18.
24. Their number.
25. Their applications to functions.
26 27. Products of substitutions.
28. Groups of substitutions.
29 32. Correlation of function and group.
34. Symmetric group.
35. Alternating group.
36 38. Construction of simple groups.
39 40. Group of order pf.
CHAPTER III.
THE DIFFERENT VALUES OF A MULTIPLE—VALUED FUNCTION AND THEIB
ALGEBRAIC RELATION TO ONE ANOTHER.
41 44. Relation of the order of a group to the number of values
of the corresponding function. 44.
viii contents.
45. Groups belonging to the different values of a function.
46 47. Transformation.
48 50. The Cauchy Sylow Theorem.
51. Distribution of the elements in the cycles of a group.
52. Substitutions which belong to all values of a function.
53. Equation for a p valued function.
55. Discriminants of the functions of a group.
56 59. Multiple valued functions, powers of which are single
valued.
CHAPTEK IV.
TRANSITIVITY AND PBIMITIVITY. SIMPLE.AND COMPOUND GROUPS.
ISOMORPHISM.
60 61. Simple transitivity. 70.
62 63. Multiple transitivity.
64. Primitivity and non primitivity.
65 67. Non primitive groups.
68. Transitive properties of groups.
69 71. Commutative substitutions; self conjugate subgroups.
72 73. Isomorphism.
74 76. Substitutions which affect all the elements.
77 80. Limits of transitivity.
81 85. Transitivity of primitive groups.
86. Quotient groups.
87. Series of composition.
88 89. Constant character of the factors of composition.
91. Construction of compound groups.
92. The alternating group is simple.
93. Groups of order pa.
94. Principal series of composition.
95. The factors of composition equal prime numbers.
96. Isomorphism.
$7 98. The degree and order equal.
$9 101. Construction of isomorphic groups.
CHAPTER V.
ALGEBRAIC RELATIONS BETWEEN FUNCTIONS BELONGING TO THE SAME
GROUP.—FAMILIES OF MULTIPLE VALUED FUNCTIONS.
103 105. Functions belonging to the same group can be rationally
expressed one in terms of another. 114
106. Families; conjugate families.
107. Subordinate families.
CONTENTS. ix
108 109. Expression of the principal functions in terms of the
subordinate.
110. The resulting equation binomial.
111. Functions of the family with non vanishing discriminant.
CHAPTER VI.
THE NUMBER OF THE VALUES OF INTEGRAL FUNCTIONS.
112. Special cases. 128.
113. Change in the form of the question.
114 115. Functions whose number of values is less than their degree.
116. Intransitive and non primitive groups.
117 121. Groups with substitutions of four elements.
122 127. General theorem of C. Jordan.
CHAPTER VII.
CERTAIN SPECIAL CLASSES OF GROUPS.
128. Preliminary theorem. 144.
129. Groups Q with r = ti = p. Cyclical groups.
130. Groups 0 with r = n=p. q.
131. Groups Q with r = n=pK
132 135. Groups which leave, at the most, one element unchanged.—
Metacyclic and semi metacyclic groups.
136. Linear fractional substitutions. Group of the modular
equations.
137 139. Groups of commutative substitutions.
CHAPTER VIII.
ANALYTICAL REPRESENTATION OP SUBSTITUTIONS. THE LINEAR GROUP.
140. The analytical representation. 160.
141. Condition for the defining function.
143. Arithmetic substitutions.
144. Geometric substitutions.
*5. Condition among the constants of a geometric substitution.
146 147. Order of the linear group.
PART II.
Application or the Theory of Substitutions to the Algebraic
Equations.
CHAPTER IX.
THE EQUATIONS OF THE SECOND, THIRD AND FOURTH DEGREES. GROUP
OF AN EQUATION. RESOLVENTS.
148. The equations of the second degree. 168.
X CONTENTS.
149. The equations of the third degree.
150. The equations of the fourth degree.
152. The general problem formulated. Galois resolvents.
153 154. Affect equations. Group of an equation.
156. Fundamental theorems on the group of an equation.
157. Group of the Galois resolvent equation.
158 160. General resolvents.
CHAPTER X.
THE CYCLOTOMIC EQUATIONS.
161. Definition and irreducibility. 180.
162. Solution of cyclic equations.
163. Investigation of the operations involved.
164 165. Special resolvents.
166. Construction of regular polygons by ruler and compass.
167. The regular pentagon.
168. The regular heptadecagon.
169 170. Decomposition of the cyclic polynomial.
CHAPTER XI.
THE ABELIAN EQUATIONS.
171 172. One root of an equation a rational function of another. 197.
173. Construction of a resolvent.
174 175. Solution of the simplest Abelian equations.
176. Employment of special resolvents for the solution.
177. Second method of solution.
178 180. Examples.
181. Abelian equations. Their solvability.
182. Their group.
183. Solution of the Abelian equations; first method.
184 186. Second method.
187. Analytical representation of the groups of primitive Abelian
equations.
188 189. Examples.
CHAPTER XII.
EQUATIONS WITH RATIONAL BELATIONS BETWEEN THREE ROOTS.
190 193. Groups analogous to the Abelian groups. 222.
194. Equations all the roots of which are rational functions of
two among them.
196. Their group in the case n =p.
197. The binomial equations.
CONTENTS. XI
199. Triad equations.
200 201. Constructions of compound triad equations.
202. Group of the triad equation for n = 7.
203 205. Group of the triad equation for n = 9
206. Hessian equation of the ninth degree.
CHAPTER XIII.
THE ALGEBBAIC SOLUTION OF EQUATIONS.
207 209. Rational domain. Algebraic functions. 240.
210 211. Preliminary theorem.
212 216. Roots of solvable equations.
217. Impossibility of the solution of general equations of higher
degrees.
218. Representation of the roots of a solvable equation.
219. The equation which is satisfied by any algebraic expression.
220 221. Changes of the roots of unity which occur in the expres¬
sions for the roots.
222 224. Solvable equations of prime degree.
CHAPTER XIY.
THE GROUP OF AN ALGEBBAIC EQUATION.
226. Definition of the group. 266.
227. Its transitivity.
228. Its primitivity.
229. Galois resolvents of general and special equations.
230. Composition of the group.
231. Resolvents.
232 234. Reduction of the solution of a compound equation.
235. Decomposition of the equation into rational factors.
236 238. Adjunction of the roots of a second equation.
CHAPTER XV.
ALGEBRAICALLY SOLVABLE EQUATIONS.
239 241. Criteria for solvability. 286.
242. Applications.
243. Abel s theorem on the decomposition of solvable equations.
244. Equations of degree ph; their group.
245. Solvable equations of degree p.
246. Solvable equations of degree p2.
248 249. Expression of all the roots in terms of a certain number of
them.
|
| any_adam_object | 1 |
| author | Netto, Eugen 1846-1919 |
| author_GND | (DE-588)116944684 |
| author_facet | Netto, Eugen 1846-1919 |
| author_role | aut |
| author_sort | Netto, Eugen 1846-1919 |
| author_variant | e n en |
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| dewey-full | 512.86 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.86 |
| dewey-search | 512.86 |
| dewey-sort | 3512.86 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., rev. by the author |
| format | Book |
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| id | DE-604.BV003713145 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:04:15Z |
| institution | BVB |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002363459 |
| oclc_num | 544975 |
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| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-83 |
| physical | XI, 304 S. |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Chelsea |
| record_format | marc |
| spelling | Netto, Eugen 1846-1919 Verfasser (DE-588)116944684 aut Substitutionentheorie und ihre Anwendungen auf die Algebra The theory of substitutions and its applications to algebra 2. ed., rev. by the author Bronx, NY Chelsea 1964 XI, 304 S. txt rdacontent n rdamedia nc rdacarrier Equations, Theory of Group theory Substitution (DE-588)4183925-0 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s Substitution (DE-588)4183925-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002363459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Netto, Eugen 1846-1919 The theory of substitutions and its applications to algebra Equations, Theory of Group theory Substitution (DE-588)4183925-0 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4183925-0 (DE-588)4001156-2 |
| title | The theory of substitutions and its applications to algebra |
| title_alt | Substitutionentheorie und ihre Anwendungen auf die Algebra |
| title_auth | The theory of substitutions and its applications to algebra |
| title_exact_search | The theory of substitutions and its applications to algebra |
| title_full | The theory of substitutions and its applications to algebra |
| title_fullStr | The theory of substitutions and its applications to algebra |
| title_full_unstemmed | The theory of substitutions and its applications to algebra |
| title_short | The theory of substitutions and its applications to algebra |
| title_sort | the theory of substitutions and its applications to algebra |
| topic | Equations, Theory of Group theory Substitution (DE-588)4183925-0 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Equations, Theory of Group theory Substitution Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002363459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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