Abstract
A torsion-free abelian group of finite rank is said to be almost completely decomposable, if there is a completely decomposable subgroup of finite index. 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. The regulator and the regulator quotient are invariants of an almost completely decomposable group.
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References
Arnold, D., Pure subgroups of finite rank completely decomposable groups, Proceedings of Abelian Group Theory (Oberwolfach), Lecture Notes 874 (1981), 1–31.
Burkhardt, R., On a special class of almost completely decomposable torsion free abelian groups, to appear.
Fuchs, L., Infinite Abelian Groups I+II, Academic Press, New York (1970, 1973).
Lady, E.L., Almost completely decomposable torsion free abelian groups, Proc. A.M.S. 45 (1974), 41–47.
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© 1984 Springer-Verlag Wien
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Krapf, KJ., Mutzbauer, O. (1984). Classification of Almost Completely Decomposable Groups. In: Göbel, R., Metelli, C., Orsatti, A., Salce, L. (eds) Abelian Groups and Modules. International Centre for Mechanical Sciences, vol 287. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2814-5_9
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DOI: https://doi.org/10.1007/978-3-7091-2814-5_9
Publisher Name: Springer, Vienna
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