Geodesic
Tensor Products and the Splitting of Abelian Groups
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 764-770

Voir la notice de l'article provenant de la source Cambridge University Press

In [2], Irwin, Khabbaz, and Rayna discuss the splitting problem for abelian groups through the use of the tensor product. Throughout the paper they make a basic assumption, namely, that the torsion subgroup contains but one primary component. Under this restriction they introduce the concept of “splitting length”, which is a positive integer indicator of how far a group is from splitting. The results obtained along these lines may be extended to groups whose torsion subgroups contain any finite number of primary components by applying the work of Oppelt [4].Irwin, Khabbaz, and Rayna [2] define the notion of a p-sequence and show that for groups A where T(A) is p-primary and A/T(A) has rank one, the existence of a torsion-free element with a p-sequence is sufficient for the group to split. 
Lawver, D. A.; Toubassi, E. H. Tensor Products and the Splitting of Abelian Groups. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 764-770. doi: 10.4153/CJM-1971-085-2
@article{10_4153_CJM_1971_085_2,
     author = {Lawver, D. A. and Toubassi, E. H.},
     title = {Tensor {Products} and the {Splitting} of {Abelian} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {764--770},
     year = {1971},
     volume = {23},
     number = {5},
     doi = {10.4153/CJM-1971-085-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-085-2/}
}
TY  - JOUR
AU  - Lawver, D. A.
AU  - Toubassi, E. H.
TI  - Tensor Products and the Splitting of Abelian Groups
JO  - Canadian journal of mathematics
PY  - 1971
SP  - 764
EP  - 770
VL  - 23
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-085-2/
DO  - 10.4153/CJM-1971-085-2
ID  - 10_4153_CJM_1971_085_2
ER  - 
%0 Journal Article
%A Lawver, D. A.
%A Toubassi, E. H.
%T Tensor Products and the Splitting of Abelian Groups
%J Canadian journal of mathematics
%D 1971
%P 764-770
%V 23
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-085-2/
%R 10.4153/CJM-1971-085-2
%F 10_4153_CJM_1971_085_2

[1] 1. Fuchs, L., Notes on abelian groups. I, Ann. Univ. Sci. Budapest 2 (1959), 5–23. Google Scholar

[2] 2. Irwin, J. M., Khabbaz, S. A., and Rayna, G., The role of the tensor product in the splitting oj abelian groups, J. Algebra U (1970), 423–442. Google Scholar

[3] 3. Kaplansky, I., Infinite abelian groups, revised edition (University of Michigan Press, Ann Arbor, 1968). Google Scholar

[4] 4. Oppelt, J. A., Mixed abelian groups, Can. J. Math. 19 (1967), 1259–1262. Google Scholar

[5] 5. Toubassi, E. H., On the splitting of mixed groups of torsion-free rank one (to appear). Google Scholar

Cité par Sources :