  We develop an approach to the character theory of certain classes of finite
and profinite groups based on the construction of a Lie algebra associated to
such a group, but without making use of the notion of a polarization which is
central to the classical orbit method. Instead, Kirillov's character formula
becomes the fundamental object of study. Our results are then used to produce
an alternate proof of the orbit method classification of complex irreducible
representations of p-groups of nilpotence class less than p, where p is a
prime, and of continuous complex irreducible representations of uniformly
powerful pro-p-groups (with a certain modification for p=2). As a main
application, we give a quick and transparent proof of the p-adic analogue of
Brown's theorem, stating that for a nilpotent Lie group over Q_p the Fell
topology on the set of isomorphism classes of its irreducible representations
coincides with the quotient topology on the set of its coadjoint orbits.
