Abstract
The splitting length of a mixed Abelian group G is defined as the smallest positive integer n such that \( \mathop \otimes \limits^n G \) splits. The task of determining the splitting length of mixed Abelian groups was formulated by Irwin, Khabbaz, and Rayna. In this paper, a criterion for determining whether \( \mathop \otimes \limits^n G \) splits for countable mixed Abelian groups G of torsion-free rank 1 is found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Fuchs, “Notes on Abelian groups. I, II,” Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 2, 5–23 (1959); Acta Math. Acad. Sci. Hungar., 11, 117–125 (1960).
L. Fuchs, Infinite Abelian Groups, Academic Press, New York (1970).
J. M. Irwin, S. A. Khabbaz, and G. Rayna, “The role of the tensor product in the splitting of Abelian groups,” J. Algebra, 14, 423–422 (1970).
L. Kulikov, “On the theory of Abelian groups of arbitrary power,” Mat. Sb., 9, 165–182 (1941).
D. A. Lawver and E. H. Toubassi, “Tensor products and the splitting of Abelian groups,” Can. J. Math., 23, No. 5, 764–770 (1971).
C. Megibben, “On mixed groups of torsion-free rank one,” Illinois J. Math., 11, 134–144 (1967).
J. Rotman, “Torsion-free and mixed Abelian groups,” Illinois J. Math., 5, 131–143 (1961).
E. H. Toubassi and D. A. Lawver, “Height-slope and splitting length of Abelian groups,” Publ. Math. Debrecen, 20, 63–71 (1973).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 7, pp. 209–221, 200.
Rights and permissions
About this article
Cite this article
Thu Thuy, P.T. Splitting length of abelian mixed groups of torsion-free rank 1. J Math Sci 164, 294–302 (2010). https://doi.org/10.1007/s10958-009-9731-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-009-9731-5