  We consider the Noether's problem on the noncommutative real rational
functions invariant under the linear action of a finite group. For abelian
groups the invariant skew-fields are always rational. We show that for a
solvable group the invariant skew-field is finitely generated. The skew-field
invariant under a linear action of a solvable group is rational if the action
is well-behaved -- given by a so-called complete representation. We determine
the groups that admit such representations and call them totally
psuedo-unramified. In the second part we study the reach of totally
psuedo-unramified groups and classify totally pseudo-unramified p-groups of
rank at most 5.
