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The Group of Extensions and Splitting Length

Published online by Cambridge University Press:  20 November 2018

E. H. Toubassi
E. H. Toubassi*
Affiliation:
University of Arizona, Tucson, Arizona
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This paper is concerned with the internal structure of Ext(Q, T) where Q is the group of rationals and T a reduced p-primary group of unbounded order. In [1] Irwin, Khabbaz, and Rayna define the splitting length of an arbitrary abelian group A, written l(A), to be the least positive integer n, otherwise infinity, such that A ⊗ . . . ⊗ A (n factors) splits. The concept of splitting length has been induced on Ext(Q, T), see [2; 5].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 879 - 883
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Irwin, J. M., Khabbaz, S. A., and G. Rayna, The role of the tensor product in the splitting of abelian groups, J. Algebra 14 (1970), 423–442.Google Scholar
2. Irwin, J. M., Khabbaz, S. A., and G. Rayna, Ona submodule of Ext, J. Algebra 19 (1971), 486–495.Google Scholar
3. Nunke, R., On the extensions of a torsion module, Pacific J. Math. 10 (1960), 597–606.Google Scholar
4. Szele, T., On the basic subgroups of abelian p-groups, Acta. Math. Acad. Sci. Hung. 5 (1954), 129–141.Google Scholar
5. Toubassi, E. H., On the group of extensions, Acta. Math. Acad. Sci. Hung. 24 (1973), 87–92.Google Scholar
6. Lawver, D. A. and Toubassi, E. H., Height-slope and splitting length of abelian groups, Publ. Math. Debrecen 20 (1973), 63–71.Google Scholar