Abstract :
Abstract. 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 ? 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 p^m - p^m-1 ? 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 1.
