  We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x
\right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general
class that map this equation into itself or into equations of a similar class.
In some cases this porous medium equation is connected with well known
equations. With the introduction of a new dependent variable this partial
differential equation can be equivalently written as a system of two equations.
Point transformations are also sought for this auxiliary system. It turns out
that in addition to the continuous point transformations that may be derived by
Lie's method, a number of discrete transformations are obtained. In some cases
the point transformations which are presented here for the single equation and
for the auxiliary system form cyclic groups of finite order.
