Orderable groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1977
|
| Ausgabe: | 1. print. |
| Schriftenreihe: | Lecture notes in pure and applied mathematics
27 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 169 S. |
| ISBN: | 0824765796 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804136093834018816 |
|---|---|
| adam_text | CONTENTS
CHAPTER I ORDERABLE GROUPS 1
1.1 Introduction 1
1.2 Definitions and Notations 2
1.3 Characterizations of Orderable
Groups 8
1.4 Relatively and Absolutely Convex
Subgroups 14
1.5 Order Automorphisms of Subgroups
of the Additive Group of the
Real Numbers 21
CHAPTER II MORE ON ORDERABLE GROUPS 25
2.1 Closure Properties 25
2.2 The Role of the Centre 26
2.3 Free Products, Direct and Free
Products with Amalgamation 33
2.4 Examples of Orderable Groups 37
2.5 Commutator Identities 44
2.6 Orderable Groups with Normal
Relatively Convex Subgroups ..... 47
CHAPTER III 0* GROUPS 53
3.1 Basic Properties of 0* Groups .... 53
3.2 Negative Results for 0* Groups ... 58
3.3 Ordered Solvable Groups with
Finite Rank 66
3.4 I* Groups 73
3.5 Other Classes Related to
0* Groups 77
CHAPTER IV R* GROUPS 79
4.1 Solvable R* Groups with Finite
Rank 79
4.2 Hypercentral by Metabelian
R* Groups 87
4.3 A Non Orderable R* Group 89
iii
CHAPTER V EMBEDDING THEOREMS AND ESCALATION
GROUPS 97
5.1 Embedding in a Perfect Group 97
5.2 Embedding in a Simple Group 98
5.3 Embedding in a Two Generator Group . . 103
5.4 Embedding in Ordered Division
Rings 105
5.5 Subgroups with Periodic Quotient . . . 108
5.6 Escalation Groups 113
CHAPTER VI ON THE NUMBER OF WAYS OF ORDERING A
GROUP 117
6.1 Groups with Finitely Many Orders . . . 117
6.2 A Family of Groups with a Countable
Infinity of Orders 124
CHAPTER VII RIGHT ORDERABLE GROUPS 127
7.1 Characterizations of Right Orderable
Groups 128
7.2 Convex Subgroups 132
7.3 Closure Properties of the Class of
Right Orderable Groups 133
7.4 C Groups 135
7.5 C* Groups 141
7.6 Extensions of Partial Right Orders . . 147
7.7 Group Rings of Right Orderable
Groups 154
APPENDIX 157
TABLE OF RESULTS ON CLOSURE OPERATIONS 161
BIBLIOGRAPHY 163
INDEX 169
iv
|
| adam_txt |
CONTENTS
CHAPTER I ORDERABLE GROUPS 1
1.1 Introduction 1
1.2 Definitions and Notations 2
1.3 Characterizations of Orderable
Groups 8
1.4 Relatively and Absolutely Convex
Subgroups 14
1.5 Order Automorphisms of Subgroups
of the Additive Group of the
Real Numbers 21
CHAPTER II MORE ON ORDERABLE GROUPS 25
2.1 Closure Properties 25
2.2 The Role of the Centre 26
2.3 Free Products, Direct and Free
Products with Amalgamation 33
2.4 Examples of Orderable Groups 37
2.5 Commutator Identities 44
2.6 Orderable Groups with Normal
Relatively Convex Subgroups . 47
CHAPTER III 0* GROUPS 53
3.1 Basic Properties of 0* Groups . 53
3.2 Negative Results for 0* Groups . 58
3.3 Ordered Solvable Groups with
Finite Rank 66
3.4 I* Groups 73
3.5 Other Classes Related to
0* Groups 77
CHAPTER IV R* GROUPS 79
4.1 Solvable R* Groups with Finite
Rank 79
4.2 Hypercentral by Metabelian
R* Groups 87
4.3 A Non Orderable R* Group 89
iii
CHAPTER V EMBEDDING THEOREMS AND ESCALATION
GROUPS 97
5.1 Embedding in a Perfect Group 97
5.2 Embedding in a Simple Group 98
5.3 Embedding in a Two Generator Group . . 103
5.4 Embedding in Ordered Division
Rings 105
5.5 Subgroups with Periodic Quotient . . . 108
5.6 Escalation Groups 113
CHAPTER VI ON THE NUMBER OF WAYS OF ORDERING A
GROUP 117
6.1 Groups with Finitely Many Orders . . . 117
6.2 A Family of Groups with a Countable
Infinity of Orders 124
CHAPTER VII RIGHT ORDERABLE GROUPS 127
7.1 Characterizations of Right Orderable
Groups 128
7.2 Convex Subgroups 132
7.3 Closure Properties of the Class of
Right Orderable Groups 133
7.4 C Groups 135
7.5 C* Groups 141
7.6 Extensions of Partial Right Orders . . 147
7.7 Group Rings of Right Orderable
Groups 154
APPENDIX 157
TABLE OF RESULTS ON CLOSURE OPERATIONS 161
BIBLIOGRAPHY 163
INDEX 169
iv |
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| id | DE-604.BV022119976 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:13Z |
| indexdate | 2024-07-09T20:50:55Z |
| institution | BVB |
| isbn | 0824765796 |
| language | English |
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| physical | 169 S. |
| publishDate | 1977 |
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| publisher | Dekker |
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| series | Lecture notes in pure and applied mathematics |
| series2 | Lecture notes in pure and applied mathematics |
| spelling | Botto Mura, Roberta Verfasser aut Orderable groups Roberta Botta Mura and Akbar Rhemtulla 1. print. New York [u.a.] Dekker 1977 169 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in pure and applied mathematics 27 Geordnete Gruppe (DE-588)4156745-6 gnd rswk-swf Geordnete Gruppe (DE-588)4156745-6 s DE-604 Rhemtulla, Akbar Verfasser aut Lecture notes in pure and applied mathematics 27 (DE-604)BV005871364 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015334726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Botto Mura, Roberta Rhemtulla, Akbar Orderable groups Lecture notes in pure and applied mathematics Geordnete Gruppe (DE-588)4156745-6 gnd |
| subject_GND | (DE-588)4156745-6 |
| title | Orderable groups |
| title_auth | Orderable groups |
| title_exact_search | Orderable groups |
| title_exact_search_txtP | Orderable groups |
| title_full | Orderable groups Roberta Botta Mura and Akbar Rhemtulla |
| title_fullStr | Orderable groups Roberta Botta Mura and Akbar Rhemtulla |
| title_full_unstemmed | Orderable groups Roberta Botta Mura and Akbar Rhemtulla |
| title_short | Orderable groups |
| title_sort | orderable groups |
| topic | Geordnete Gruppe (DE-588)4156745-6 gnd |
| topic_facet | Geordnete Gruppe |
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