A property of B 2 -groups

Kulumani M. Rangaswamy

Commentationes Mathematicae Universitatis Carolinae (1994)

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

Abstract

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It is shown, under ZFC, that a B 2 -group has the interesting property of being ℵ 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.

How to cite

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Rangaswamy, 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

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

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