A characterization of powerful p-groups

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

COHOMOLOGY OF UNIFORMLY POWERFUL p-GROUPS

In this paper we will study the cohomology of a family of p-groups associated to Fp-Lie algebras. More precisely we study a category BGrp of p-groups which will be equivalent to the category of Fp-bracket algebras (Lie algebras minus the Jacobi identity). We then show that for a group G in this category, its Fp-cohomology is that of an elementary abelian p-group if and only if it is associated ...

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 ${}leq 4$ 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 $p$...

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 $p$-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 $p$...

some inequalities for nilpotent multipliers of powerful p-groups