Unitary units in group rings of groups of order \(16\)
Let \(U(ZG)\) denote the group of units of the integral group ring of a finite group \(G\). To give a set of generators of this group is, in general, a difficult problem. As a compromise, it has been a major trend in the area to look for a set of generators of a subgroup of finite index. The so-called bicyclic and Bass cyclic units constitute such a set in many cases. Recently \textit{A. A. Bovdi} and \textit{S. K. Sehgal} [Publ. Mat., Barc. 36, No. 1, 197-204 (1992; Zbl 0778.16013)] have considered groups \(G\) such that all bicyclic units in \(ZG\) are unitary. In particular, there are five non-Hamiltonian groups of order 16 with that property. In this note it is shown that for these five groups, the Bass cyclic and unitary units generate a subgroup of finite index in \(U(ZG)\).
scientific article; zbMATH DE number 645227