The norm $N(G)$ of a group $G$ is the intersection of the normalizers of all subgroups in $G$. In this paper, the norm is generalized by studying on Sylow subgroups and ${\mathscr{H}}$-subgroups in finite groups which is denoted by $C(G)$ and $A(G)$, respectively. It is proved that the generalized norms $A(G)$ and $C(G)$ are all equal to the hypercenter of $G$.

中文翻译：

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关于有限群的广义范数

规范$ñ(G)$一组的$G$是所有子群的归一化器的交集$G$. 在本文中，范数通过研究 Sylow 子群和${\mathscr{H}}$- 有限群中的子群，表示为$C(G)$和$\mathrm{一个}(G)$， 分别。证明了广义规范$\mathrm{一个}(G)$和$C(G)$都等于$G$.