Almost Completely Decomposable Groups

Almost Completely Decomposable Groups

By: A. Mader (author)Hardback

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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.

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1. Notation and Background 2. Basics and Completely Decomposable Groups 3. Cyclic Essential Extensions 4. Regulating Subgroups and Regulators 5. Local-Global Relationships 6. Groups with Cyclic Regulating 7. Completely Decomposable Summands 8. Anti-Representations 8. Near-Isomorphism and Type-Isomorphism 9. Fundamental Decomposition Theorems 10. Finite Essential Extensions 11. Representing Matrices 12. Classification 13. Direct Decompositions of Block-Rigid crq-Groups 14. In Search for Good Categories 15. Associated Structures 16. Literature

Product Details

  • publication date: 09/03/2000
  • ISBN13: 9789056992255
  • Format: Hardback
  • Number Of Pages: 366
  • ID: 9789056992255
  • weight: 798
  • ISBN10: 9056992252

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