Torsion completeness of the group of normalized units in modular group rings. (English) Zbl 0823.16022

Let \(p\) be a prime, let \(G\) be an abelian \(p\)-group and let \(R\) be a commutative ring with 1. Denote by \(V(RG)\) the group of normalized units of the group algebra \(RG\). The author proves that the group \(V(RG)\) is torsion complete if and only if \(G\) is bounded. The case where \(G\) is an arbitrary abelian group seems to be still unresolved.


16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
20K10 Torsion groups, primary groups and generalized primary groups
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)