Arithmetical similarities: prime decomposition and finite group theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1998
|
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 275 S. graph. Darst. |
| ISBN: | 0198535988 |
Internformat
MARC
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| 245 | 1 | 0 | |a Arithmetical similarities |b prime decomposition and finite group theory |c Norbert Klingen |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1998 | |
| 300 | |a IX, 275 S. |b graph. Darst. | ||
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| 490 | 0 | |a Oxford mathematical monographs | |
| 650 | 4 | |a Algebraic number theory | |
| 650 | 4 | |a Finite groups | |
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| 650 | 0 | 7 | |a Artinsche L-Funktion |0 (DE-588)4143138-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1825578092223004672 |
|---|---|
| adam_text |
Contents
Introduction 1
I Prime decomposition 3
§1 Prime decomposition and group theory 3
a. Prime ideals and residue degrees 3
b. Galois extensions and Frobenius automorphisms 6
c. Residue degrees and cycle lengths 11
§2 Prime decomposition and zeta functions 15
a. Dedekind's zeta function 15
b. Dirichlet density 17
§3 Class field theory and density theorems 20
a. Abelian extensions 20
b. Dirichlet L series 22
§4 Artin L functions 25
a. Definition 26
b. Functoriality 29
c. Induction property 30
II Kronecker equivalence 37
§1 Introduction and group theoretic description 37
a. Kronecker sets 37
b. Bauerian extensions 42
c. Kronecker equivalence 46
§2 Examples of Kronecker classes 51
a. Infinite Kronecker classes 52
b. Towers in Kronecker classes 55
c. Extensions of prime degree within Kronecker classes 59
viii Contents
§3 The socle of Kronecker classes 61
a. Minimal fields in Kronecker classes 62
b. Socles of Kronecker classes 64
c. Socles with Galois group An and Sn 68
III Arithmetical equivalence 75
§1 Zeta functions and characters 75
a. Decomposition type and arithmetic invariants 75
b. Examples of arithmetically equivalent fields 85
c. Computational results 90
§2 Relations between arithmetical and Kronecker equivalence 94
a. Splitting Galois groups 94
b. 2 Transitive Galois groups and fields of prime degree 99
c. Decomposition types in Kronecker equivalent fields 101
§3 Radical extensions 105
a. Bauerian extensions 106
b. Non trivial socles 109
c. Explicit generators 118
§4 Arithmetical equivalence and symmetric designs 124
a. Symmetric designs 124
b. Automorphism groups of symmetric designs 126
c. Kronecker equivalence for 2 transitive Galois groups 130
IV Arithmetical homomorphisms 133
§1 Linearly equivalent permutation representations 133
a. The critical primes 133
b. Arithmetical homomorphisms 138
c. Cohomology groups 142
§2 Class numbers and regulators 145
a. Galois modules 145
b. Idele and ideal groups 148
c. Class number and regulator quotients 155
§3 Explicit bounds for class number quotients 163
a. Radical extensions 163
b. 2 Transitive symmetric designs 173
c. General linear groups 176
Contents ix
V Kroneckerian fields 189
§1 Quadratic extensions 190
a. Jehne's criterion 190
b. The series An and PSL2(g) 196
c. Brandl's approach and the sporadic groups 199
d. Saxl's proof for classical groups 200
§2 Quartic extensions 202
a. Galois Kronecker classes and covering subgroups 202
b. Covering subgroups of index 4 205
c. Kroneckerian extensions of degree 4 211
§3 Generic extensions of degree n 215
a. Group theoretic reduction 216
b. Covering JFp spaces 219
c. Covering sets of functions 224
VI Variations 227
§1 Weak Kronecker equivalence and norm groups 227
a. Weak Kronecker equivalence 227
b. Norm groups 231
§2 Ramification indices and the adele ring 234
a. Ramification and locally isomorphic number fields 234
b. Isomorphic adele rings 236
§3 Arithmetical similarity in characteristic p 241
a. Global fields in positive characteristic 241
b. Arithmetical equivalence, adele rings and isogenies 245
§4 Arithmetical similarity of algebras 248
a. Semisimple algebras 248
b. Group algebras 250
§5 Isospectral manifolds 250
a. Length spectra 251
b. Eigenvalue spectra of Laplace operators 252
Bibliography 255
List of notation 264
Index 271 |
| any_adam_object | 1 |
| author | Klingen, Norbert 1945- |
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| dewey-full | 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.74 |
| dewey-search | 512.74 |
| dewey-sort | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2025-03-03T13:02:17Z |
| institution | BVB |
| isbn | 0198535988 |
| language | English |
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| physical | IX, 275 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Clarendon Press |
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| series2 | Oxford mathematical monographs |
| spelling | Klingen, Norbert 1945- Verfasser (DE-588)1012439461 aut Arithmetical similarities prime decomposition and finite group theory Norbert Klingen Oxford Clarendon Press 1998 IX, 275 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Algebraic number theory Finite groups Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Artinsche L-Funktion (DE-588)4143138-8 gnd rswk-swf Primzahlzerlegung (DE-588)4175717-8 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s Artinsche L-Funktion (DE-588)4143138-8 s Primzahlzerlegung (DE-588)4175717-8 s Endliche Gruppe (DE-588)4014651-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008123912&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klingen, Norbert 1945- Arithmetical similarities prime decomposition and finite group theory Algebraic number theory Finite groups Endliche Gruppe (DE-588)4014651-0 gnd Artinsche L-Funktion (DE-588)4143138-8 gnd Primzahlzerlegung (DE-588)4175717-8 gnd Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4143138-8 (DE-588)4175717-8 (DE-588)4190764-4 |
| title | Arithmetical similarities prime decomposition and finite group theory |
| title_auth | Arithmetical similarities prime decomposition and finite group theory |
| title_exact_search | Arithmetical similarities prime decomposition and finite group theory |
| title_full | Arithmetical similarities prime decomposition and finite group theory Norbert Klingen |
| title_fullStr | Arithmetical similarities prime decomposition and finite group theory Norbert Klingen |
| title_full_unstemmed | Arithmetical similarities prime decomposition and finite group theory Norbert Klingen |
| title_short | Arithmetical similarities |
| title_sort | arithmetical similarities prime decomposition and finite group theory |
| title_sub | prime decomposition and finite group theory |
| topic | Algebraic number theory Finite groups Endliche Gruppe (DE-588)4014651-0 gnd Artinsche L-Funktion (DE-588)4143138-8 gnd Primzahlzerlegung (DE-588)4175717-8 gnd Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Algebraic number theory Finite groups Endliche Gruppe Artinsche L-Funktion Primzahlzerlegung Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008123912&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT klingennorbert arithmeticalsimilaritiesprimedecompositionandfinitegrouptheory |