Trivial units in commutative group rings of \(G\times C_n\) (Q6585988)

A famous result due to \N\textit{G. Higman} [Proc. Lond. Math. Soc. (2) 46, 231--248 (1940; Zbl 0025.24302)] states that the torsion units of the integral group ring \(\mathbb{Z}G\) of an arbitrary abelian group \(G\) are always trivial being of the form \(\pm G\).\N\NThe article under review is devoted to the study of some special cases of this statement, especially to studying the trivial units in commutative group rings of the group \(G\times C_n\), where \(G\) is an abelian group and \(C_n\) is the standard cyclic group of order \(p^n\) for some \(n\in \mathbb{N}\). The main results are stated and proved Theorems 1, 2, 3 and 4, respectively.