Search Results

Now showing 1 - 1 of 1

Citation - WoS: 13
Citation - Scopus: 14
Poor and Pi-Poor Abelian Groups
(Taylor and Francis Ltd., 2017) Alizade, Rafail; Büyükaşık, Engin
In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to (Formula presented.) , where P is the set of prime integers. We also prove that pi-poor abelian groups exist. Namely, it is proved that the direct sum of U(ℕ), where U ranges over all nonisomorphic uniform abelian groups, is pi-poor. Moreover, for a pi-poor abelian group M, it is shown that M can not be torsion, and each p-primary component of M is unbounded. Finally, we show that there are pi-poor groups which are not poor, and vise versa.

Mathematics / Matematik