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Vladikavkazskii Matematicheskii Zhurnal, 2007, Volume 9, Number 1, Pages 30–37
(Mi vmj85)
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This article is cited in 3 scientific papers (total in 3 papers)
A note on weakly $\aleph_1$-separable $p$-groups
P. V. Danchev Plovdiv State University «Paissii Hilendarski», Plovdiv, Bulgaria
Abstract:
It is well-known by Hill-Griffith that there exist $\aleph_1$-separable $p$-primary groups which are not direct sums of cycles. A problem of challenging interest, mainly due to Hill (Rocky Mount. J. Math., 1971), is under what extra circumstances on the group structure this holds untrue, that is every $\aleph_1$-separable $p$-group is a direct sum of cyclic groups. We prove here that any weakly $\aleph_1$-separable $p$-group of cardinality not exceeding $\aleph_1$ is quasi-complete precisely when it is a bounded direct sum of cycles, thus partly answering the posed question in the affirmative.
Key words:
weakly $\aleph_1$-separable groups, quasi-complete groups, torsion-complete groups, bounded groups.
Received: 03.07.2006
Citation:
P. V. Danchev, “A note on weakly $\aleph_1$-separable $p$-groups”, Vladikavkaz. Mat. Zh., 9:1 (2007), 30–37
Linking options:
https://www.mathnet.ru/eng/vmj85 https://www.mathnet.ru/eng/vmj/v9/i1/p30
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Abstract page: | 304 | Full-text PDF : | 88 | References: | 49 | First page: | 1 |
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