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Title: On direct sums of $\text{B}^{(1)}$-groups -- II (English)
Author: De Vivo, Clorinda
Author: Metelli, Claudia
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 47
Issue: 2
Year: 2006
Pages: 189-202
Category: math
Summary: $\operatorname{B}^{(1)}$-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, {\it On direct sums of $\operatorname{B}^{(1)}$-groups\/}, Comment. Math. Univ. Carolinae {\bf 34} (1993), 587--591, the problem of direct sums of $\operatorname{B}^{(1)}$-groups was discussed, and a necessary and sufficient condition was given for the direct sum of two $\operatorname{B}^{(1)}$-groups to be a $\operatorname{B}^{(1)}$-group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable direct summands of $\operatorname{B}^{(1)}$-groups. (English)
Keyword: Butler group
Keyword: $\operatorname{B}^{(1)}$-group
Keyword: tent
Keyword: direct decomposition
Keyword: finite algorithm
MSC: 20K15
idZBL: Zbl 1106.20041
idMR: MR2241526
Date available: 2009-05-05T16:56:42Z
Last updated: 2012-04-30
Stable URL:
Related article:
Reference: [FII] Fuchs L.: Infinite Abelian Groups. Vol.II.Academic Press London - New York (1973). Zbl 0257.20035, MR 0349869
Reference: [A] Arnold D.M.: Abelian groups and representations of finite partially ordered sets.CMS books in Mathematics Springer New York (2000). Zbl 0959.16011, MR 1764257
Reference: [AV] Arnold D.M., Vinsonhaler C.: Finite rank Butler groups: a survey of recent results.Abelian groups (Curaçao, 1991) Dekker New York (1993), 17-41. Zbl 0804.20043, MR 1217256
Reference: [M] Metelli C.: On direct sums of ${an{B^{(1)}}}$-groups.Comment. Math. Univ. Carolinae 34 (1993), 587-591. MR 1243091
Reference: [DVM4] De Vivo C., Metelli C.: Decomposing ${an{B^{(1)}}}$-groups: an algorithm..Comm. Algebra 30 (2002), 12 5621-5637. MR 1941915
Reference: [DVM8] De Vivo C., Metelli C.: On degenerate ${an{B^{(2)}}}$-groups.Houston J. Math., to appear. MR 2247900
Reference: [CDVM] Caruso I., De Vivo C., Metelli C.: Partition bases for ${an{B^{(1)}}}$ appear on Abelian Groups, Rings and Modules; Lecture Notes in Pure and Applied Mathematics, Taylor and Francis, 2005.


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