# On direct sums of ${\mathcal{B}}^{\left(1\right)}$-groups

Commentationes Mathematicae Universitatis Carolinae (1993)

- Volume: 34, Issue: 3, page 587-591
- ISSN: 0010-2628

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topMetelli, Claudia. "On direct sums of $\mathcal {B}^{(1)}$-groups." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 587-591. <http://eudml.org/doc/247481>.

@article{Metelli1993,

abstract = {A necessary and sufficient condition is given for the direct sum of two $\mathcal \{B\}^\{(1)\}$-groups to be (quasi-isomorphic to) a $\mathcal \{B\}^\{(1)\}$-group. A $\mathcal \{B\}^\{(1)\}$-group is a torsionfree Abelian group that can be realized as the quotient of a finite direct sum of rank 1 groups modulo a pure subgroup of rank 1.},

author = {Metelli, Claudia},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {$\mathcal \{B\}^\{(1)\}$-groups; Butler groups of finite rank; completely decomposable torsionfree group of finite rank; Butler groups; completely decomposable group; direct sums},

language = {eng},

number = {3},

pages = {587-591},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On direct sums of $\mathcal \{B\}^\{(1)\}$-groups},

url = {http://eudml.org/doc/247481},

volume = {34},

year = {1993},

}

TY - JOUR

AU - Metelli, Claudia

TI - On direct sums of $\mathcal {B}^{(1)}$-groups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1993

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 34

IS - 3

SP - 587

EP - 591

AB - A necessary and sufficient condition is given for the direct sum of two $\mathcal {B}^{(1)}$-groups to be (quasi-isomorphic to) a $\mathcal {B}^{(1)}$-group. A $\mathcal {B}^{(1)}$-group is a torsionfree Abelian group that can be realized as the quotient of a finite direct sum of rank 1 groups modulo a pure subgroup of rank 1.

LA - eng

KW - $\mathcal {B}^{(1)}$-groups; Butler groups of finite rank; completely decomposable torsionfree group of finite rank; Butler groups; completely decomposable group; direct sums

UR - http://eudml.org/doc/247481

ER -

## References

top- Fuchs L., Metelli C., On a class of Butler groups, Manuscripta Math 71 (1991), 1-28. (1991) Zbl0765.20026MR1094735
- Höfling B., On direct summands of Butler ${\mathcal{B}}^{\left(1\right)}$-groups, to appear in Comm. in Algebra. MR1215549
- Fuchs L., Infinite Abelian Groups, Vol. II, Academic Press, London-New York, 1973. Zbl0338.20063MR0349869
- Albrecht U.F., Goeters H.P., Megibben C., Zero-one matrices with an application to Abelian groups, to appear in Rend. Sem. Mat. Univ. Padova. Zbl0809.20046MR1257128
- Goeters H.P., Megibben C., Quasi-isomorphism and $\mathbb{Z}\left(2\right)$ representations for a class of Butler groups, preprint. MR1876211
- Goeters H.P., Ullery W., Butler groups and lattices of types, Comment. Math. Univ. Carolinae 31 (1990), 613-619. (1990) Zbl0717.20039MR1091358
- Goeters H.P., Ullery W., Quasi-summands of a certain class of Butler groups, to appear in Proceedings of the 1991 Curacao Conference. Zbl0806.20043MR1217267

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