Unitary subgroup of the multiplicative group of the integral group ring of a cyclic group
Let U(ZG) be the multiplicative group of the integral group ring ZG of a cyclic group G, where \(| G| =2^{kt}\) (k\(\geq 1)\). If \(f: G\to U(Z)\) is a homomorphism, then the element \(u=\sum_{g\in G}\alpha_ gg\in U(ZG)\) is called f-unitary if \(u^{-1}=u^ f=\sum_{g\in G}\alpha_ gf(g)g^{-1}\) or \(u^{-1}=-u^ f\). The subgroup \(U_ f(ZG)\) of all f-unitary elements of U(ZG) is called the f-unitary subgroup of U(ZG). In this paper the author continues his research on the structure of the subgroup \(U_ f(ZG)\) when f(G)\(\neq \{1\}\) and \(t>1\).
scientific article; zbMATH DE number 4027694