Generators of Large Subgroups of Units of Integral Group Rings of Nilpotent Groups

Let G be a finite nilpotent group so that all simple components (D)n × n, n ≥ 2 of QG satisfy the congruence subgroup theorem. Suppose that for all odd primes p dividing |G| the Hamiltonian quaternions H split over the pth cyclotomic field Q(ζp). Then new units B3 are introduced so that 〈 B1, B2, B′2, B3〉 is of finite index in U(ZG).