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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

16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
Full Text: DOI
[1] S. P. Novikov, ?The algebraic structure and properties of the Hermitian analogs of K-theory over rings with involution from the point of view of the Hamiltonian formalism. Some applications to differential topology and theory of characteristic classes. II,? Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 3, 475-500 (1970).
[2] A. A. Bovdi, ?The unitary subgroup and the congruence-subgroup of the multiplicative group of an integral group ring,? Dokl. Akad. Nauk SSSR,284, No. 5 1041-1044 (1985). · Zbl 0594.16002
[3] A. A. Bovdi, ?The unitary property of the multiplicative group of an integral group ring,? Mat. Sb.,119, No. 3, 387-400 (1982). · Zbl 0511.16009
[4] H. Bass, ?The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups,? Topology,4, 391-410 (1966). · Zbl 0166.02401
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