On the generalized norms of finite groups.

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 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. [ABSTRACT FROM AUTHOR]