  In this article, we define a new k-adic series transformation called
Z-transformation and probe into its fixed point and periodicity. We extend the
number field of the transform period problem to a wider k-adic field. Different
constraints are imposed on k, then different periodic columns are formed after
finite Z-transformations. We obtain that their periodic sequences are M1= {1,2}
and M2={1,2}\cup {n_0}\cup {n'} respectively after derivation. As an
application, it can provide a reference for C problems in more complex
algebraic ystems.
