Constructing units in commutative group rings
Let \(A\) be a finite Abelian group and \(U(A)\) be the unit group of the integral group ring \(\mathbb{Z} A\). In 1965 Bass constructed generators for a free Abelian subgroup of finite index in \(U(A)\). In 1990 Hoechsmann and Ritter described another such construction with the advantage of producing subgroups of much lower index in \(U(A)\), but the disadvantage of being constrained to \(p\)-groups \(A\) of odd order. This paper extends the second procedure to arbitrary \(A\), and clarifies its relation to the first one.
scientific article; zbMATH DE number 91445