在抽象代数中，一个群的换位子群或导群，是指由这个群的所有交换子所生成的子群，记作[G,G]、G′或G 。每个群都对应着一个确定的交换子群。在一个群G的所有正规子群中，交换子群G′是使得G对它的商群为交换群的最小子群。在某种意义上，交换子群提供了群G的可交换程度。因为从交换子的定义： ，如果x与y交换，那幺[x,y]=e。一个群内可交换的元素越多，交换子就越少，交换子群也就越小。可交换群的交换子群为平凡群{e}。

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.

The commutator subgroup is important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian. In other words, G/N is abelian if and only if N contains the commutator subgroup. So in some sense it provides a measure of how far the group is from being abelian; the larger the commutator subgroup is, the "less abelian" the group is.