Central units of integral group rings of monomial groups.

Abstract

In this paper, it is proved that the group generated by Bass units contains a subgroup of finite index in the group of central units Z(U(ZG)) of the integral group ring ZG for a subgroup closed monomial group G with the property that every cyclic subgroup of order not a divisor of 4 or 6 is subnormal in G. If G is a generalized strongly monomial group, then it is also shown that the group generated by generalized Bass units contains a subgroup of finite index in Z(U(ZG)). Furthermore, for a generalized strongly monomial group G, the rank of Z(U(ZG)) is determined. The formula so obtained is in terms of generalized strong Shoda pairs of G.