Let $G$ be a finite group and $\mathfrak{F}$ a class of finite groups. A subgroup $H$ of $G$ is said to be $\mathfrak{F}$-permutable in $G$ if there exists a subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\cap T) H_{G}/H_{G}$ is contained in the $\mathfrak{F}$-hypercenter $Z_{\infty}^{\mathfrak{F}}(G/H_{G})$ of $G/H_{G}$. By using this new concept, we establish some new criteria for a group $G$ to be soluble.