A note on weakly \(\aleph_1\)-separable \(p\)-groups

Danchev P. V.
Владикавказский математический журнал. . Том 9. 2007 г.. Выпуск 1.

Аннотация:
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.

Ключевые слова: weakly \(\aleph_1\)-separable groups, quasi-complete groups, torsion-complete groups, bounded groups.

Язык статьи: Английский Загрузить полный текст