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Conditions for p-supersolubility and p-nilpotency of finite soluble groups
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 $G$.