It is well-known by Hill-Griffith that there exist ℵ1-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 ℵ1-separable p-group is a direct sum of cyclic groups. We prove… (More)
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