  In this paper we investigate Uludag's method for constructing new curves
whose fundamental groups are central extensions of the fundamental group of the
original curve by finite cyclic groups.
  In the first part, we give some generalizations to his method in order to get
new families of curves with controlled fundamental groups. In the second part,
we discuss some properties of groups which are preserved by these methods.
Afterwards, we describe precisely the families of curves which can be obtained
by applying the generalized methods to several types of plane curves. We also
give an application of the general methods for constructing new Zariski pairs.
