Torsion points of small order on superelliptic curves

In this talk a superelliptic curve  means a cyclic cover of the projective line.
We discuss generalizations of well known properties of torsion points of order 3 on elliptic curves
in characteristic 3 to certain superelliptic curves with special reference to hyperelliptic ones.

This is a report on a joint work with Boris Bekker (St. Petersburg).