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 {}\leq ۴ for p=۲) are‎ ‎contained in the k-th term of the upper central series of P‎, ‎then the p-length of‎ ‎G is at most ۲m+۱‎, ‎where m is the greatest integer such that‎ ‎p^m-p^{m-۱}\leq k‎, ‎and the exponent of the image of P in G/O_{p',p}(G) is at most‎ ‎p^m‎. ‎It is also proved that if P is a powerful‎ ‎p-group‎, ‎then the p-length of G is equal to ۱‎.