Almost completely decomposable groups
An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general theory of acd groups has been developed and a suitable weakening of isomorphism, Lady's near-isomorphism, has been established as the rightconcept for studyi…
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- Full title :Almost completely decomposable groups / by A Mader.
Summary
An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general theory of acd groups has been developed and a suitable weakening of isomorphism, Lady's near-isomorphism, has been established as the rightconcept for studying acd groups. A number of important classes of acd groups has been successfully classified. Direct sum decompositions of acd groups are preserved under near-isomorphism and the well-known pathological decompositions can actually be surveyed in special cases.
Read More ↓Edition Statements
- Publication Date:2000.
- Edition:First edition
Publication Statements
- Publisher(s):CRC Press, an imprint of Taylor and Francis
- Place of Publication:Boca Raton, FL
- Language:eng
- Publication Date:2000.
The Physical Object
- Description:1 online resource (366 pages)
Edition Identifiers
- ISBN:9781482287486, 148228748X
- oclc:on1073083018
- LC Classification:QA180
- Dewey Decimal:512/.2
Table of Contents
Chapter Introduction -- chapter Acknowledgements -- chapter 1 Notation and Background -- chapter 2 Basics and Completely Decomposable Groups -- chapter 3 Cyclic Essential Extensions -- chapter 4 Regulating Subgroups and Regulators -- chapter 5 Local-global Relationships -- chapter 6 Groups with Cyclic Regulating Quotient -- chapter 7 Completely Decomposable Summands -- chapter 8 Anti?Representations -- chapter 9 Near-Isomorphism and Type-Isomorphism -- chapter 10 Fundamental Decomposition Theorems -- chapter 11 Finite Essential Extensions -- chapter 12 Classification -- chapter 13 Direct Decompositions of Block-Rigid crq-Groups -- chapter 14 In Search for Good Categories -- chapter 15 Associated Structures -- chapter 16 Literature.
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