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Bibliographic Details
Main Authors:	Botto Mura, Roberta (Author), Rhemtulla, Akbar (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Dekker 1977
Edition:	1. print.
Series:	Lecture notes in pure and applied mathematics 27
Subjects:	Geordnete Gruppe
Online Access:	Inhaltsverzeichnis
Physical Description:	169 S.
ISBN:	0824765796

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MARC


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Record in the Search Index

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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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author	Botto Mura, Roberta Rhemtulla, Akbar
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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
url	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
volume_link	(DE-604)BV005871364
work_keys_str_mv	AT bottomuraroberta orderablegroups AT rhemtullaakbar orderablegroups

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