Geodesic
Splitting length of Abelian mixed groups of torsion-free rank 1
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 209-221 
Pham Thi Thu Thuy. Splitting length of Abelian mixed groups of torsion-free rank 1. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 209-221. http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a17/
@article{FPM_2008_14_7_a17,
     author = {Pham Thi Thu Thuy},
     title = {Splitting length of {Abelian} mixed groups of torsion-free rank~1},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {209--221},
     year = {2008},
     volume = {14},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a17/}
}
TY  - JOUR
AU  - Pham Thi Thu Thuy
TI  - Splitting length of Abelian mixed groups of torsion-free rank 1
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2008
SP  - 209
EP  - 221
VL  - 14
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a17/
LA  - ru
ID  - FPM_2008_14_7_a17
ER  - 
%0 Journal Article
%A Pham Thi Thu Thuy
%T Splitting length of Abelian mixed groups of torsion-free rank 1
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 209-221
%V 14
%N 7
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a17/
%G ru
%F FPM_2008_14_7_a17

Voir la notice de l'article provenant de la source Math-Net.Ru

Splitting length of a mixed Abelian group $G$ is defined as the smallest positive integer $n$ such that $\bigotimes\limits^nG$ 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 $\bigotimes\limits^nG$ splits for countable mixed Abelian groups $G$ of torsion-free rank 1 is found.

[1] Kulikov L. Ya., “K teorii abelevykh grupp proizvolnoi moschnosti”, Mat. sb., 9(51):1 (1941), 165–181 | MR | Zbl

[2] Fuks L., Beskonechnye abelevy gruppy, Mir, M., 1974

[3] Fuchs L., “Notes on Abelian groups. I”, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 2 (1959), 5–23 ; “II”, Acta Math. Acad. Sci. Hungar., 11 (1960), 117–125 | MR | Zbl | DOI | MR | Zbl

[4] Irwin J. M., Khabbaz S. A., Rayna G., “The role of the tensor product in the splitting of Abelian groups”, J. Algebra, 14 (1970), 423–422 | DOI | MR

[5] Lawver D. A., Toubassi E. H., “Tensor products and the splitting of Abelian groups”, Can. J. Math., 23:5 (1971), 764–770 | DOI | MR | Zbl

[6] Megibben C., “On mixed groups of torsion-free rank one”, Illinois J. Math., 11 (1967), 134–144 | MR | Zbl

[7] Rotman J., “Torsion-free and mixed Abelian groups”, Illinois J. Math., 5 (1961), 131–143 | MR | Zbl

[8] Toubassi E. H., Lawver D. A., “Height-slope and splitting length of Abelian groups”, Publ. Math. Debrecen., 20 (1973), 63–71 | MR | Zbl