A Note on Countable Butler Groups

David M. Arnold; Kulumani M. Rangaswamy

Bollettino dell'Unione Matematica Italiana (2007)

• Volume: 10-B, Issue: 3, page 605-611
• ISSN: 0392-4041

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Abstract

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An example of a countable Butler group that is not a pure subgroup of a completely decomposable group was published in 1986. Recently, an error in the proof was discovered. This note includes a corrected argument, as well as a proof that this group has no pure precobalanced subgroups of rank one.

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Arnold, David M., and Rangaswamy, Kulumani M.. "A Note on Countable Butler Groups." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 605-611. <http://eudml.org/doc/290391>.

@article{Arnold2007,
abstract = {An example of a countable Butler group that is not a pure subgroup of a completely decomposable group was published in 1986. Recently, an error in the proof was discovered. This note includes a corrected argument, as well as a proof that this group has no pure precobalanced subgroups of rank one.},
author = {Arnold, David M., Rangaswamy, Kulumani M.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {605-611},
publisher = {Unione Matematica Italiana},
title = {A Note on Countable Butler Groups},
url = {http://eudml.org/doc/290391},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Arnold, David M.
AU - Rangaswamy, Kulumani M.
TI - A Note on Countable Butler Groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 605
EP - 611
AB - An example of a countable Butler group that is not a pure subgroup of a completely decomposable group was published in 1986. Recently, an error in the proof was discovered. This note includes a corrected argument, as well as a proof that this group has no pure precobalanced subgroups of rank one.
LA - eng
UR - http://eudml.org/doc/290391
ER -

References

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1. ARNOLD, M. DAVID, Notes on Butler groups and balanced extensions, Bull. U.M.I. (6) 5-A (1986), 175-184. Zbl0601.20050MR850285
2. ARNOLD, M. DAVID, Abelian Groups and Representations of Finite Partially Ordered Sets, CMS Books in Mathematics, Springer-Verlag, New York, 2000. Zbl0959.16011MR1764257DOI10.1007/978-1-4419-8750-1
3. BICAN, L. - SALCE, L., Butler groups of infinite rank, Abelian Group Theory, Lecture Notes in Math.1006, Springer-Verlag, New York, 1983. Zbl0515.20035MR722617DOI10.1007/BFb0103701
4. BUTLER, M. C. R., A class of torsion-free abelian groups of finite rank, Proc. London Math. Soc. (3) 15 (1965), 680-698. Zbl0131.02501MR218446DOI10.1112/plms/s3-15.1.680
5. FUCHS, L. - METELLI, C., Countable Butler groups, Abelian Groups and Non-commutative Rings, Contemporary Math.130 (1992), 133-143. Zbl0769.20025MR1176115DOI10.1090/conm/130/1176115
6. GIOVANNITTI, A. J., Torsion-free abelian groups with precobalanced finite rank pure subgroups, Abelian Groups, Lecture Notes in Pure and Applied Mathematics Vol. 146, Marcel Dekker, New York, 1993, 157-166. Zbl0801.20034MR1217266
7. GIOVANNITTI, A. J. - GOETERS, H. P. - METELLI, C., Cobalanced exact sequences, Commen. Math. Univ. Carolinae, 4 (1989), 637-641. Zbl0693.20055MR1045891
8. GIOVANNITTI, A. J. - RANGASWAMY, K. M., Precobalanced subgroups of abelian groups, Comm. in Algebra19 (1) (1991), 249-269. Zbl0717.20040MR1092561DOI10.1080/00927879108824139
9. MADER, A. - MUTZBAUER, O. - RANGASWAMY, K. M. A., A generalization of Butler groups, Abelian Group Theory, Contemporary Mathematics, 171 (1994), 257-275. Zbl0821.20033MR1293146DOI10.1090/conm/171/01777

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