The integral group ring
of a group
G has only trivial central units, if the only central units of
are
for
z in the center of
G. We show that the order of a finite solvable group
G with this property, can only be divisible by the primes
2,
3,
5 and
7, by linking this to inverse semi-rational groups and extending one result on this class of
... [Show full abstract] groups. We also classify the Frobenius groups whose integral group rings have only trivial central units.