Free subgroups in the group of units of group rings. II (Q1085250)

[Part I, cf. Can. Math. Bull. 27, 309-312 (1984; Zbl 0513.16007).] Let G be a finite group and R the ring of integers of an algebraic number field K. The author investigates the occurrence of free subgroups in the group of units U(RG) of the group ring of G over R. He first shows that when G is finite and K is totally real then U(RG) does not contain a free subgroup of rank two if and only if G is either abelian or a Hamiltonian 2-group; if K is not totally real then this happens only when G is abelian. Then, he considers the case where G is the extension of a solvable torsion group T by a torsion-free nilpotent group. In this case, U(RG) does not contain a free subgroup of rank two if and only if every idempotent in KT is central in KG (a condition studied by \textit{S. P. Coelho} [Proc. Edinb. Math. Soc., II. Ser. 30, 69-72 (1987; Zbl 0588.16005)] and either T is abelian or K is totally real and T a Hamiltonian 2-group.