Conditions for $p$-supersolubility and $p$-nilpotency of finite soluble groups
Volume 133 / 2013
Colloquium Mathematicum 133 (2013), 85-98
MSC: 20D10, 20D20.
DOI: 10.4064/cm133-1-6
Abstract
Let $\mathfrak {Z}$ be a complete set of Sylow subgroups of a group $G$. A subgroup $H$ of $G$ is called $\mathfrak {Z}$-permutably embedded in $G$ if every Sylow subgroup of $H$ is also a Sylow subgroup of some $\mathfrak {Z}$-permutable subgroup of $G$. By using this concept, we obtain some new criteria of $p$-supersolubility and $p$-nilpotency of a finite group.
