Orderable Groups (Lecture Notes in Pure and Applied Mathematics)

Title Page......Page 2 Copyright Page......Page 3 CONTENTS......Page 4 1.1 Introduction......Page 6 1.2 Definitions and Notations......Page 7 1.3 Characterizations of Orderable Groups......Page 13 1.4 Relatively and Absolutely Convex Subgroups......Page 19 1.5 Order-Automorphisms of Subgroups of the Additive Group of the Real Numbers......Page 26 2.1 Closure Properties......Page 30 2.2 The Role of the Centre......Page 31 2.3 Free Products, Direct and Free Products with Amalgamation......Page 38 2.4 Examples of Orderable Groups......Page 42 2.5 Commutator Identities......Page 49 2.6 Orderable Groups with Normal Relatively Convex Subgroups......Page 52 3.1 Basic Properties of 0*-Groups......Page 58 3.2 Negative Results for 0*-Groups......Page 63 3.3 Ordered Solvable Groups with Finite Rank......Page 71 3.4 I*-Groups......Page 78 3.5 Other Classes Related to 0*-Groups......Page 82 4.1 Solvable R*-Groups with Finite Rank......Page 84 4.2 Hypercentral-by-Metabelian R*-Groups......Page 92 4.3 A Non-Orderable R*-Group......Page 94 5.1 Embedding in a Perfect Group......Page 102 5.2 Embedding in a Simple Group......Page 103 5.3 Embedding in a Two-Generator Group......Page 108 5.4 Embedding in Ordered Division Rings......Page 110 5.5 Subgroups with Periodic Quotient......Page 113 5.6 Escalation Groups......Page 118 6.1 Groups with Finitely Many Orders......Page 122 6.2 A Family of Groups with a Countable Infinity of Orders......Page 129 CHAPTER VII RIGHT-ORDERABLE GROUPS......Page 132 7.1 Characterizations of Right-Orderable Groups......Page 133 7.2 Convex Subgroups......Page 137 7.3 Closure Properties of the Class of Right-Orderable Groups......Page 138 7.4 Groups......Page 140 7.5 C*-Groups......Page 146 7.6 Extensions of Partial Right-Orders......Page 152 7.7 Group Rings of Right-Orderable Groups......Page 159 APPENDIX......Page 162 TABLE OF RESULTS ON CLOSURE OPERATIONS......Page 166 BIBLIOGRAPHY......Page 168 INDEX......Page 174