On direct sums of ℬ ( 1 ) -groups

Claudia Metelli

Commentationes Mathematicae Universitatis Carolinae (1993)

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

Abstract

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A necessary and sufficient condition is given for the direct sum of two ℬ ( 1 ) -groups to be (quasi-isomorphic to) a ℬ ( 1 ) -group. A 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.

How to cite

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Metelli, 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

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  1. Fuchs L., Metelli C., On a class of Butler groups, Manuscripta Math 71 (1991), 1-28. (1991) Zbl0765.20026MR1094735
  2. Höfling B., On direct summands of Butler ℬ ( 1 ) -groups, to appear in Comm. in Algebra. MR1215549
  3. Fuchs L., Infinite Abelian Groups, Vol. II, Academic Press, London-New York, 1973. Zbl0338.20063MR0349869
  4. 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
  5. Goeters H.P., Megibben C., Quasi-isomorphism and ℤ ( 2 ) representations for a class of Butler groups, preprint. MR1876211
  6. Goeters H.P., Ullery W., Butler groups and lattices of types, Comment. Math. Univ. Carolinae 31 (1990), 613-619. (1990) Zbl0717.20039MR1091358
  7. 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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