# A property of ${B}_{2}$-groups

Commentationes Mathematicae Universitatis Carolinae (1994)

- Volume: 35, Issue: 4, page 627-631
- ISSN: 0010-2628

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topRangaswamy, Kulumani M.. "A property of $B_2$-groups." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 627-631. <http://eudml.org/doc/247582>.

@article{Rangaswamy1994,

abstract = {It is shown, under ZFC, that a $B_2$-group has the interesting property of being $\aleph _0$-prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on $B_2$-groups.},

author = {Rangaswamy, Kulumani M.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {torsion-free abelian groups; Butler groups; $B_2$-groups; $\aleph _0$-prebalanced subgroups; completely decomposable groups; separative subgroups; Butler groups; -groups; -prebalanced subgroups; separative subgroups; pure subgroup; completely decomposable groups},

language = {eng},

number = {4},

pages = {627-631},

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

title = {A property of $B_2$-groups},

url = {http://eudml.org/doc/247582},

volume = {35},

year = {1994},

}

TY - JOUR

AU - Rangaswamy, Kulumani M.

TI - A property of $B_2$-groups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1994

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

VL - 35

IS - 4

SP - 627

EP - 631

AB - It is shown, under ZFC, that a $B_2$-group has the interesting property of being $\aleph _0$-prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on $B_2$-groups.

LA - eng

KW - torsion-free abelian groups; Butler groups; $B_2$-groups; $\aleph _0$-prebalanced subgroups; completely decomposable groups; separative subgroups; Butler groups; -groups; -prebalanced subgroups; separative subgroups; pure subgroup; completely decomposable groups

UR - http://eudml.org/doc/247582

ER -

## References

top- Albrecht U., Hill P., Butler groups of infinite rank and Axiom-3, Czech. Math. J. 37 (1987), 293-309. (1987) Zbl0628.20045MR0882600
- Bican L., Fuchs L., Subgroups of Butler groups, to appear. Zbl0802.20045MR1378188
- Dugas M., Hill P., Rangaswamy K.M., Butler groups of infinite rank, Trans. Amer. Math. Soc. 320 (1990), 643-664. (1990) Zbl0708.20018MR0963246
- Fuchs L., Infinite Abelian Groups, vol. 2, Academic Press, New York, 1973. MR0349869
- Fuchs L., Butler Groups of Infinite Rank, to appear. Zbl0842.20045MR1316995
- Hill P., Megibben C., Pure subgroups of torsion-free groups, Trans. Amer. Math. Soc. 303 (1987), 765-778. (1987) Zbl0627.20028MR0902797
- Rangaswamy K.M., A homological characterization of abelian ${B}_{2}$-groups, Proc. Amer. Math. Soc., to appear. MR1186993

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