Almost Completely Decomposable Groups

1. Auflage 2000
ISBN: 978-90-5699-225-5
Verlag: Taylor & Francis Ltd

Buch, Englisch, 366 Seiten, Format (B × H): 157 mm x 240 mm, Gewicht: 767 g

Reihe: Algebra, Logic and Applications

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.

Autoren/Hrsg.

Mader, A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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

Über Autor(innen)

A Mader