On p-soluble groups with a generalized p-central or powerful Sylow p-subgroup

Let g be a finite p-soluble group, and p a sylow p-subgroup of g. it is proved that if all elements of p of order p (or of order 6 4 for p = 2) are contained in the k-th term of the upper central series of p, then the p-length of g is at most 2m+1, where m is the greatest integer such that pm - pm-1 6 k, and the exponent of the image of p in g=op0;p(g) is at most pm. it is also proved that if p is a powerful p-group, then the p-length of g is equal to 1