  A maximal abelian normal subgroup A in a nilpotent group N is
self-centralizing. This makes their role an important one in determining the
structure of the nilpotent group. For example if A is finite then N is also
finite.
  In the free nilpotent group of class 2 such a group is always a cyclic
extension of the center. However this need not be true in an arbitrary finitely
generated class two nilpotent group. We show that three generator nilpotent
groups violating this condition can be easily found. However in the case when
there are four or more generators certain conditions must hold.
