Geodesic
On direct sums of $\text{B}^{(1)}$-groups -- II
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 189-202 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

$\operatorname{B}^{(1)}$-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, {\it On direct sums of $\operatorname{B}^{(1)}$-groups\/}, Comment. Math. Univ. Carolinae {\bf 34} (1993), 587--591, the problem of direct sums of $\operatorname{B}^{(1)}$-groups was discussed, and a necessary and sufficient condition was given for the direct sum of two $\operatorname{B}^{(1)}$-groups to be a $\operatorname{B}^{(1)}$-group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable direct summands of $\operatorname{B}^{(1)}$-groups.
$\operatorname{B}^{(1)}$-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, {\it On direct sums of $\operatorname{B}^{(1)}$-groups\/}, Comment. Math. Univ. Carolinae {\bf 34} (1993), 587--591, the problem of direct sums of $\operatorname{B}^{(1)}$-groups was discussed, and a necessary and sufficient condition was given for the direct sum of two $\operatorname{B}^{(1)}$-groups to be a $\operatorname{B}^{(1)}$-group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable direct summands of $\operatorname{B}^{(1)}$-groups.
Classification : 20K15
Keywords: Butler group; $\operatorname{B}^{(1)}$-group; tent; direct decomposition; finite algorithm 
@article{CMUC_2006_47_2_a0,
     author = {De Vivo, Clorinda and Metelli, Claudia},
     title = {On direct sums of $\text{B}^{(1)}$-groups -- {II}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {189--202},
     year = {2006},
     volume = {47},
     number = {2},
     mrnumber = {2241526},
     zbl = {1106.20041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a0/}
}
TY  - JOUR
AU  - De Vivo, Clorinda
AU  - Metelli, Claudia
TI  - On direct sums of $\text{B}^{(1)}$-groups -- II
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 189
EP  - 202
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a0/
LA  - en
ID  - CMUC_2006_47_2_a0
ER  - 
%0 Journal Article
%A De Vivo, Clorinda
%A Metelli, Claudia
%T On direct sums of $\text{B}^{(1)}$-groups -- II
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 189-202
%V 47
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a0/
%G en
%F CMUC_2006_47_2_a0
De Vivo, Clorinda; Metelli, Claudia. On direct sums of $\text{B}^{(1)}$-groups -- II. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 189-202. http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a0/