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 ${}leq 4$ 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 ‎$p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...

let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-sub-group of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ 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 $p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...