Fibonacci Length of an Efficiently Presented Metabelian p-Group

For every integer n =1 and every odd prime p, an efficient presentation is given for the wreath product ZpζZp^n which, is of nilpotency class (p - l)n+1. Moreover,the Fibonacci length is proved to be 8 x 3n when p = 3, and in general, k(p) x v,where k(p) is the period of Fibonacci length modulo p (the Wall number of p).