  In this article we discuss a certain p-adic analogue of classical Schwarzian
triangle groups, an analogue which is related to Mumford's uniformization of
p-adic analytic curves. p-adic Schwarzian triangle groups are defined to be the
Galois groups of analytic coverings over projective line with precisely 3
branch points. We say that a p-adic triangle group is of Mumford type if the
corresponding universal covering is given by a certain locally compact analytic
subspace in projective line, related to Mumford's uniformization. The main
theorem provides a complete classification of p-adic triangle groups of Mumford
type; our list of these groups contains some of the arithmetic p-adic triangle
groups which are discussed by Yves Andre. Notably, we deduce that p-adic
triangle groups of Mumford type exist only if p=2,3,5.
