Central subgroup

In mathematics, in the field of group theory, a subgroup of a group is termed central if it lies inside the center of the group.

Given a group $G$ , the center of $G$ , denoted as $Z(G)$ , is defined as the set of those elements of the group which commute with every element of the group. The center is a characteristic subgroup and is also an abelian group (because, in particular, all elements of the center must commute with each other). A subgroup $H$ of $G$ is termed central if $H \leq Z(G)$ .

单词	Central subgroup
释义	Central subgroup 英语百科 Central subgroup In mathematics, in the field of group theory, a subgroup of a group is termed central if it lies inside the center of the group. Given a group $G$ , the center of $G$ , denoted as $Z(G)$ , is defined as the set of those elements of the group which commute with every element of the group. The center is a characteristic subgroup and is also an abelian group (because, in particular, all elements of the center must commute with each other). A subgroup $H$ of $G$ is termed central if $H \leq Z(G)$ .
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