Criteria for unit groups in commutative group rings. (English) Zbl 1120.16302
Summary: Suppose \(G\) is an arbitrary Abelian group and \(F\) is a field of \(\text{char\,}F=p\neq 0\). In the present paper criteria are found the group of all units \(UF[G]\) in the group ring \(F[G]\) and its subgroup \(VF[G]\) of normed units to belong to some central classes of Abelian groups under minimal restrictions on \(F\) and \(G\).
MSC:
| 16U60 | Units, groups of units (associative rings and algebras) |
| 16S34 | Group rings |
| 20K10 | Torsion groups, primary groups and generalized primary groups |
| 20K20 | Torsion-free groups, infinite rank |
| 20K21 | Mixed groups |
