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 p(n), 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. (C) 2015 Elsevier Inc. All rights reserved.