# 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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topArnold, 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

top- ARNOLD, M. DAVID, Notes on Butler groups and balanced extensions, Bull. U.M.I. (6) 5-A (1986), 175-184. Zbl0601.20050MR850285
- 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
- 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
- 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
- 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
- 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
- GIOVANNITTI, A. J. - GOETERS, H. P. - METELLI, C., Cobalanced exact sequences, Commen. Math. Univ. Carolinae, 4 (1989), 637-641. Zbl0693.20055MR1045891
- GIOVANNITTI, A. J. - RANGASWAMY, K. M., Precobalanced subgroups of abelian groups, Comm. in Algebra19 (1) (1991), 249-269. Zbl0717.20040MR1092561DOI10.1080/00927879108824139
- 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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