Integral group rings with all central units trivial
  The object of study in this paper is the finite groups whose integral group rings have only trivial central units. Prime-power groups and metacyclic groups with this property are characterized. Metacyclic groups are classified according to the central height of the unit groups of their integral group rings. 
Gurmeet K. Bakshi, Sugandha Maheshwary and Inder Bir S. Passi
math.RA