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Almost completely decomposable groups

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Published by Gordon and Breach Science Publishers in Amsterdam, The Netherlands .
Written in English

Subjects:

  • Abelian groups.,
  • Decomposition (Mathematics)

Book details:

Edition Notes

Includes bibliographical references (p. 343-346) and index.

StatementAdolf Mader.
SeriesAlgebra, logic, and applications ;, v. 13
Classifications
LC ClassificationsQA180 .M34 2000
The Physical Object
Paginationx, 354 p. ;
Number of Pages354
ID Numbers
Open LibraryOL3630021M
ISBN 109056992252
LC Control Number2002421693
OCLC/WorldCa41257172

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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 Cited by: Book Description 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. 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 . Almost completely decomposable groups can be described in terms of integral matrices and in terms of anti-representations in finite modules over proper quotient rings of the ring of integers.

A completely decom — posable subgroup of an almost completely decomposable group of minimal index is called regulating subgroup by Lady [4]. The intersection of all regulating subgroups of A is the regulator R= R(A). Burkhardt [2] proved, that the regulator is completely decomposable. Almost completely decomposable groups are torsion-free finite extensions of completely decomposable groups of finite rank. We answer completely and in a constructive fashion the question when an. For almost completely decomposable groups, however, we do have the follow-ing weaker theorem: Theorem 6. If G is an almost completely decomposable group and G = A @ H = B @ K where A, B are r-homogeneous and H, K have no rank 1 summands of type r, then A ; B. Proof. Note that A and B are necessarily completely decomposable groups. Almost completely decomposable torsion free abelian groups Proc. Amer. Math. Soc. 45(), pp. 41 - This was the first paper I ever wrote completely on my own. I started it during August, , just after getting my degree at New Mexico State. I finished it sometime before the end of the fall semester

ALMOST COMPLETELY DECOMPOSABLE GROUPS A. MADĚR, O. MUTZBAUER AND C. VINSONHALER 1. Introduction. All groups in this paper are tacitly assumed to be abelian. An almost completely decomposable group is a torsion-free group of finite rank that contains a completely decomposable group as a subgroup of finite index. Let X be such a group and . Almost completely decomposable groups We begin with the necessary definitions. A completely decomposable group (abelian is always assumed) is a torsion-free group that is isomorphic to a finite direct sum of subgroups of the additive rationals, st completely decomposable group is any torsion-free group that.   Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.   Almost completely decomposable groups with a regulating regulator and a p-primary regulator quotient are is shown that there are indecomposable such groups of arbitrarily large rank provided that the critical typeset contains some basic configuration and the exponent of the regulator quotient is sufficiently large.