  We study the wellposedness of the master equation for a second-order mean
field games with the Grushin type diffusion. In order to do this, we obtain the
properties of its solution by investigating a degenerate mean field games
system for which there exists an equivalent characterization with the master
equation. The crucial points of this paper are to explore some regularities of
solutions to two types of linear degenerate partial differential equations and
a kind of degenerate linear coupled system so as to derive the existence of
solutions to the master equation.
