Units of group rings of groups of order 16

Let G be a finite group, (Z G ) the group of units of the integral group ring Z G and 1 (Z G ) the subgroup of units of augmentation 1. In this paper, we are primarily concerned with the problem of describing constructively (Z G ) for particular groups G. This has been done for a small number of groups (see 11 for an excellent survey), and most recently Jespers and Leal 3 described (Z G ) for several 2-groups. While the situation is clear for all groups of order less than 16, not all groups of order 16 were discussed in their paper. Our main aim is to complete the description of (Z G ) for all groups of order 16. Since the structure of the unit group of abelian groups is very well known (see for example 10), we are only interested in the non-abelian case.