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Unitary subgroup of the multiplicative group of the integral group ring of a cyclic group. (English. Russian original) Zbl 0632.16010
Math. Notes 41, 265-268 (1987); translation from Mat. Zametki 41, No. 4, 469-474 (1987).
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 \(t>1\).
Reviewer: S.V.Mihovski

MSC:
16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
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