在抽象代数中，群G的中心Z(G)是所有在G中和G的所有元素可交换的元素的集合。精确的讲：

注意Z(G)是一个G的子群— 若x和y在Z(G)中，则对于每个g（属于G）， (xy)g = x(yg) = x(gy) = (xg)y = (gx)y = g(xy) 所以xy也在Z(G)中。同样的论证对于逆操作也成立。

而且， Z(G)是一个G的可交换子群，也是G的正规子群，甚至是G的严格特征子群，但不总是完全特征的。

G的中心是整个G 当且仅当G是可交换群。另一个极端是，群可以是无中心的，若Z(G)是平凡群。

In abstract algebra, the center of a group G, denoted Z(G), is the set of elements that commute with every element of G. In set-builder notation,

The center is a subgroup of G, which by definition is abelian (that is, commutative). As a subgroup, it is always normal, and indeed characteristic, but it need not be fully characteristic. The quotient group G / Z(G) is isomorphic to the group of inner automorphisms of G.