With A. A. Kirillov’s work on
the representations of nilpotent lie groups, a new chapter in the theory of group
representations opened. Subsequent papers of Bernat, Moore and Auslander-Kostant
have further demonstrated the power of the methods introduced by Kirillov. The
purpose of this paper is to begin an extension of these methods in yet another
direction. Specifically, the object here is to calculate the primitive ideal spaces of the
groups indicated in the title.