  We initiate the study of some pro-p-groups arising from infinite-dimensional
Lie theory. These groups are completions of some subgroups of incomplete
Kac-Moody groups over finite fields, with respect to various completions of
algebraic or geometric origin. We show topological finite generation for the
pro-p Sylow subgroups in many complete Kac-Moody groups. This implies abstract
simplicity of the latter groups. We also discuss with the question of
(non-)linearity of these pro-p groups.
