On the index of a free abelian subgroup in the group of central units of an integral group ring

Let Z(U(Z[G])) denote the group of central units in the integral group ring Z[G] of a finite group G. A bound on the index of the subgroup generated by a virtual basis in Z(U(Z[G])) is computed for a class of strongly monomial groups. The result is illustrated with application to the groups of order pn, p prime, n≤4. The rank of Z(U(Z[G])) and the Wedderburn decomposition of the rational group algebra of these p-groups have also been obtained.