Akademik Veri Yönetim Sistemi
Algebra and Discrete Mathematics, cilt.37, sa.2, ss.262-274, 2024 (ESCI)
It is known that if the unit group of an integral group ring ZG is trivial, then the unit group of Z(G × C2) is trivial as well [3]. The aim of this study is twofold: firstly, to identify rings R that are D-adapted for the direct product D = G × H of abelian groups G and H, such that the unit group of the ring R(G × H) is trivial. Our second objective is to investigate the necessary and sufficient conditions on both the ring R and the direct factors of D to satisfy the property that the normalized unit group V (RD) is trivial in the case where D is one of the groups G × C3, G × K4 or G × C4, where G is an arbitrary finite abelian group, Cn denotes a cyclic group of order n and K4 is Klein 4-group. Hence, the study extends the related result in [18].