Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T15:32:33.259Z Has data issue: false hasContentIssue false
  • English
  • Français

Regulating hulls of almost completely decomposable groups

Part of: Abelian groups

Published online by Cambridge University Press:  09 April 2009

A. Mader  and
C. Vinsonhaler
A. Mader
Affiliation:
University of HawaiiHonolulu, HI 96822, USA
C. Vinsonhaler
Affiliation:
University of ConnecticutStorrs, CT 06269, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note investigates torsion-free abelian groups G of finite rank which embed, as subgroups of finite index, in a finite direct sum C of subgroups of the additive group of rational numbers. Specifically, we examine the relationship between G and C when the index of G in C is minimal. Some properties of Warfield duality are developed and used (in the case that G is locally free) to relate our results to earlier ones by Burkhardt and Lady.

MSC classification

Secondary: 20K15: Torsion-free groups, finite rank
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 2 , April 1993 , pp. 143 - 155
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Arnold, D., ‘Pure subgroups of completely decomposable groups’, in: Abelian Group Theory Proceedings, Oberwolfach 1981, Lecture Notes in Mathematics 874, (Springer, Berlin, 1981) pp. 1–31.Google Scholar
[2]Arnold, D. and Vinsonhaler, C., ‘Pure subgroups of finite rank completely completely decomposable groups, II’, in Abelian Group Theory, Proceedings, Honolulu 1982/83, Lecture Notes in Mathematics 1006 (Springer, Berlin, 1983) pp. 97–143.CrossRefGoogle Scholar
[3]Arnold, D. and Vinsonhaler, C., ‘Duality and invariants for Butler groups’, Pacific J. Math. 148 (1991), 1–10.CrossRefGoogle Scholar
[4]Baer, R., ‘Abelian groups without elements of finite order’, Duke Math. J. 3 (1937), 68–122.CrossRefGoogle Scholar
[5]Burkhardt, R., ‘On a special class of almost completely decomposable groups’, in: Abelian Groups and Modules, Proceedings of the Udine Conference 1984, CISM 287 (Springer, New York, 1984), pp. 141–150.Google Scholar
[6]Krapf, K. J. and Mutzbauer, O., ‘Classification of almost completely decomposable groups’, in: Abelian Groups and Modules, Proceedings of the Udine Conference 1984, CISM 287 (Springer, New York, 1984), 151–162.Google Scholar
[7]Lady, E. L., ‘Almost completely decomposable torsion-free groups’, Proc. Amer. Math. Soc. 45 (1974), 41–47.CrossRefGoogle Scholar
[8]Lady, E. L., ‘Extension of scalars for torsion free modules over Dedekind domains’, in: Symposia Mathematica Vol. XXIII (Academic Press, San Diego, 1979), pp. 287–305.Google Scholar
[9]Lady, E. L., ‘Warfield duality and rank-one quasi-summands of tensor products of finite rank locally free modules over Dedekind domains’, J. Algebra 121 (1989), 129–138.CrossRefGoogle Scholar
[10]Reid, J. D., ‘Warfield duality and Irreducible Groups’, preprint (to appear in Warfield Commemorative Volume).Google Scholar
[11]Warfield, R. B. Jr, ‘Homomorphisms and duality for torsion-free groups’, Math Z. 107 (1968), 189–200.CrossRefGoogle Scholar