  We define the position of an irreducible complex character of a finite group
as an alternative to the degree. We then use this to define three classes of
groups: PR-groups, IPR-groups and weak IPR-groups. We show that IPR-groups and
weak IPR-groups are solvable and satisfy the Taketa inequality (ie, that the
derived length of the group is at most the number of degrees of irreducible
complex characters of the group), and we show that any M-group is a weak
IPR-group. We also show that even though PR-groups need not be solvable, they
cannot be perfect.
