  In a finite real reflection group, the reflection length of each element is
equal to the codimension of its fixed space, and the two coincident functions
determine a partial order structure called the absolute order. In complex
reflection groups, the reflection length is no longer always equal to the
codimension of fixed space, and the two functions give rise to two different
partial orders on the group. We characterize the elements $w$ in the
combinatorial family $G(m, p, n)$ of complex reflection groups for which the
intervals below $w$ in these two posets coincide. We also explore the
relationship between this property and other natural properties of elements in
complex reflection groups; some general theory of posets arising from
subadditive functions on groups; and the particular case of subadditive
functions on the symmetric group.
