Periodic locally compact groups: a study of a class of totally disconnected topological groups
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2019]
|
| Series: | De Gruyter studies in mathematics
Volume 71 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | LIII, 301 Seiten Illustrationen |
| ISBN: | 9783110598476 3110598477 |
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MARC
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| 100 | 1 | |a Herfort, Wolfgang |e Verfasser |0 (DE-588)136125514 |4 aut | |
| 245 | 1 | 0 | |a Periodic locally compact groups |b a study of a class of totally disconnected topological groups |c Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a LIII, 301 Seiten |b Illustrationen | ||
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Record in the Search Index
| _version_ | 1804179060248543232 |
|---|---|
| adam_text | CONTENTS
PREFACE* VII
OVERVIEW* XV
PART I:
BACKGROUND INFORMATION ON LOCALLY COMPACT GROUPS
INTRODUCTION * 3
1 LOCALLY COMPACT SPACES AND GROUPS
* 5
1.1 THE PRESENCE OF MANY COMPACT OPEN SUBGROUPS * 5
1.2 THE HYPERSPACE OF CLOSED SUBGROUPS
SUB{G) OF 6 * 9
1.2.1 THE CHABAUTY SPACE OF A COMPACTLY RULED GROUP * 11
1.3 SEMIDIRECT PRODUCTS * 13
2 PERIODIC LOCALLY COMPACT GROUPS AND THEIR SYLOW THEORY * 19
2.1 NORMAL O-SUBGROUPS* 22
2.2 NORMAL O-SYLOW SUBGROUPS * 25
2.3 A SCHUR-ZASSENHAUS THEOREM * 26
2.4 THE FIXED POINT THEOREM *
33
2.5 PAIRWISE COMMUTINGP-SYLOW SUBGROUPS * 38
2.6 SYLOW BASES IN INDUCTIVELY PROSOLVABLE GROUPS * 43
3 ABELIAN PERIODIC GROUPS
* 47
3.1 BRACONNIER S THEOREM * 47
3.2 PRELIMINARIES ABOUT THE P RANK * 50
3.3 LOCALLY COMPACT ABELIAN TORSION GROUPS * 52
3.3.1 A NONSPLIT EXTENSION OF A REDUCED LOCALLY COMPACT ABELIAN P-GROUP
BY
Q P
-----
55
3.4 PURITY USED PARTIALLY * 67
3.5 LOCALLY COMPACT ABELIAN DIVISIBLE GROUPS * 69
3.6 TORSION-FREENESS AND DIVISIBILITY IN P-GROUPS * 72
3.6.1 SPLITTING IN TORSION-FREE P-GROUPS * 78
3.6.2 THE LARGEST DIVISIBLE SUBGROUP * 79
3.7 DENSE DIVISIBLE SUBGROUPS * 83
3.8 NONSPLITTING OF QP IN THE PRESENCE OF TORSION * 86
3.9 DIVISIBLE TORSION GROUPS * 91
3.10 THE P RANK OF A LOCALLY COMPACT ABELIAN P-GROUP * 93
3.11 STRUCTURE OF LOCALLY COMPACT P-GROUPS OF FINITE P RANK * 96
4 SCALAR AUTOMORPHISMS AND THE MASTERGRAPH * 101
4.1 ON SCALAR AUTOMORPHISMS * 103
4.1.1 THE STRUCTURE OF ZP FOR P * 2 * 105
4.1.2 THE STRUCTURE OF Z 2* 108
4.2 THE STRUCTURE OF THE GROUP OF SCALAR AUTOMORPHISMS * 110
4.3 A BIPARTITE GRAPH FOR SCALAR ACTION ON A PERIODIC LOCALLY COMPACT
ABELIAN
GROUP * 114
4.3.1 GEOMETRIC PROPERTIES OF THE MASTERGRAPH * 115
4.3.2 THE STRUCTURE OF Z X AND THE PRIME MASTERGRAPH * 116
4.3.3 THE SYLOW DECOMPOSITION O FZ (N )X INDEXED BY Q * 118
4.3.4 THE STRUCTURE OF SAUT(A) AND ITS PRIME GRAPH Q(A) * 119
4.3.5 THE STRUCTURE OF A SCALAR ACTION AND ITS PRIME GRAPH * 121
5 INDUCTIVELY MONOTHETIC GROUPS * 127
5.1 CLASSIFYING INDUCTIVELY MONOTHETIC SUBGROUPS * 128
5.1.1 THE BUILD-UP OF N-PROCYCLIC GROUPS FROM OPEN PROCYCLIC
SUBGROUPS * 130
5.1.2 INDUCTIVELY MONOTHETIC GROUPS AND DIVISIBILITY * 131
5.2 THE SUBSPACE OF INDUCTIVELY MONOTHETIC SUBGROUPS * 137
5.3 ON DIVISIBILITY AND Z P * 138
5.4 THE EXTENSIONS OF A LOCALLY COMPACT GROUP BY A N-PROCYCLIC GROUP *
139
PART II:
NEAR ABELIAN GROUPS
INTRODUCTION * 149
6 THE DEFINITION OF NEAR ABELIAN GROUPS * 151
6.1 BASIC DEFINITIONS * 151
7 IMPORTANT CONSEQUENCES OF THE DEFINITIONS * 157
7.1 PERIODICITY OF NEAR ABELIAN GROUPS * 157
7.2 NEAR ABELIAN P-GROUPS * 159
7.3 NONTRIVIAL NEAR ABELIAN GROUPS * 160
7.4 A FIRST GLANCE AT THE SYLOW THEORY OF PERIODIC NEAR ABELIAN GROUPS *
163
7.5 THE EXISTENCE OF SCALING SUBGROUPS * 167
7.6 SINGULAR NEAR ABELIAN GROUPS * 176
8 TRIVIAL NEAR ABELIAN GROUPS * 179
8.1 THE SUBSET 6(G) IN A TRIVIAL NEAR ABELIAN GROUP * 182
8.2 GENERAL STRUCTURE OF TRIVIAL NEAR ABELIAN GROUPS * 186
9 THE CLASS OF NEAR ABELIAN GROUPS
* 191
9.1 CLOSED SUBGROUPS * 191
9.2 QUOTIENT GROUPS
-----
193
9.3 PROJECTIVE LIMITS * 194
9.4 INDUCTIVE LIMITS * 196
10 THE SYLOW STRUCTURE OF PERIODIC NONTRIVIAL NEAR ABELIAN GROUPS AND
THEIR
PRIME GRAPHS
* 203
10.1 MORE ON THE SYLOW STRUCTURE OF C6(A) * 212
10.2 DESCRIBING GD FOR A PERIODIC A-NONTRIVIAL NEAR ABELIAN GROUP * 216
10.3 THE ALGEBRAIC COMMUTATOR GROUP OF A PERIODIC NEAR ABELIAN
GROUP * 217
11 A LIST OF EXAMPLES
* 219
PART III:
APPLICATIONS
INTRODUCTION * 227
12 CLASSIFYING TOPOLOGICALLY QUASIHAMILTONIAN GROUPS * 229
12.1 GENERALITIES * 229
12.2 THE P-GROUP CASE * 231
12.3 THE PERIODIC CASE * 233
12.4 THE NONPERIODIC CASE * 235
13 LOCALLY COMPACT GROUPS WITH A MODULAR SUBGROUP LATTICE * 241
13.1 GENERALITIES * 241
13.2 THE P-GROUP CASE * 245
13.2.1 ABELIAN P-GROUPS * 245
13.2.2 NONPERIODIC LOCALLY COMPACT ABELIAN GROUPS * 249
13.3 IWASAWA (P, Q)-FACTORS * 249
13.4 THE PERIODIC CASE * 252
13.5 A SUMMARY OF PERIODIC LOCALLY COMPACT TOPOLOGICAL /W-GROUPS * 257
13.6 THE NONPERIODIC CASE * 259
14 STRONGLY TOPOLOGICALLY QUASIHAMILTONIAN GROUPS * 263
14.1 HISTORICAL BACKGROUND * 263
14.2 MORE NOTATION * 264
14.3 GENERALITIES * 264
14.4 THE ABELIAN CASE * 265
14.4.1 THE ABELIAN P-GROUP CASE * 266
14.4.2 CLASSIFYING PERIODIC ABELIAN GROUPS
14.5 THE NONABELIAN SITUATION * 274
14.5.1 THE PERIODIC CASE * 274
14.5.2 THE NONPERIODIC CASE * 283
BIBLIOGRAPHY * 289
LIST OF SYMBOLS * 295
INDEX * 297
|
| any_adam_object | 1 |
| author | Herfort, Wolfgang Hofmann, Karl H. 1932- Russo, Francesco G. |
| author_GND | (DE-588)136125514 (DE-588)115780734 (DE-588)1156790948 |
| author_facet | Herfort, Wolfgang Hofmann, Karl H. 1932- Russo, Francesco G. |
| author_role | aut aut aut |
| author_sort | Herfort, Wolfgang |
| author_variant | w h wh k h h kh khh f g r fg fgr |
| building | Verbundindex |
| bvnumber | BV045284026 |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)1077591286 (DE-599)DNB1154612597 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045284026 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:13:51Z |
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| isbn | 9783110598476 3110598477 |
| language | English |
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| physical | LIII, 301 Seiten Illustrationen |
| publishDate | 2019 |
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| spelling | Herfort, Wolfgang Verfasser (DE-588)136125514 aut Periodic locally compact groups a study of a class of totally disconnected topological groups Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo Berlin ; Boston De Gruyter [2019] © 2019 LIII, 301 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics Volume 71 Lokal kompakte Gruppe (DE-588)4168094-7 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Gruppentheorie Lokal kompakte Gruppe Topologische Gruppe Lokal kompakte Gruppe (DE-588)4168094-7 s Topologische Gruppe (DE-588)4135793-0 s 1\p DE-604 Hofmann, Karl H. 1932- Verfasser (DE-588)115780734 aut Russo, Francesco G. Verfasser (DE-588)1156790948 aut Erscheint auch als Online-Ausgabe, EPUB 978-3-11-059908-4 Erscheint auch als Online-Ausgabe, PDF 978-3-11-059919-0 De Gruyter studies in mathematics Volume 71 (DE-604)BV000005407 71 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030671500&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Herfort, Wolfgang Hofmann, Karl H. 1932- Russo, Francesco G. Periodic locally compact groups a study of a class of totally disconnected topological groups De Gruyter studies in mathematics Lokal kompakte Gruppe (DE-588)4168094-7 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4168094-7 (DE-588)4135793-0 |
| title | Periodic locally compact groups a study of a class of totally disconnected topological groups |
| title_auth | Periodic locally compact groups a study of a class of totally disconnected topological groups |
| title_exact_search | Periodic locally compact groups a study of a class of totally disconnected topological groups |
| title_full | Periodic locally compact groups a study of a class of totally disconnected topological groups Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo |
| title_fullStr | Periodic locally compact groups a study of a class of totally disconnected topological groups Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo |
| title_full_unstemmed | Periodic locally compact groups a study of a class of totally disconnected topological groups Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo |
| title_short | Periodic locally compact groups |
| title_sort | periodic locally compact groups a study of a class of totally disconnected topological groups |
| title_sub | a study of a class of totally disconnected topological groups |
| topic | Lokal kompakte Gruppe (DE-588)4168094-7 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Lokal kompakte Gruppe Topologische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030671500&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
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