A note on weakly \Aleph_1-separable P-groups

A note on weakly \Aleph_1-separable P-groups

Автор: Danchev peteR. V.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 1 т.9, 2007 года.

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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.

Weakly \aleph_1-separable groups, quasi-complete groups, torsion-complete groups, bounded groups

Короткий адрес: https://sciup.org/14318587

IDR: 14318587

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