在数学的群论中，一个群称为完满群（又称完全群，但完全群可以指另一种群），如果这个群等于其换位子群；或者等价地说，如果这个群的阿贝尔商群只有平凡群。

最小的完满群是交错群。一般而言，任何非阿贝尔单群都是完满群。因为一个群的换位子群是正规子群，所以单群的换位子群只能是其自身或平凡子群。而换位子群的对应商群必是阿贝尔群，因此如果一个群是非阿贝尔，其换位子群不能为平凡子群。

不是单群的完满群的例子有特殊线性群SL(2,5)，即是在有限域上的所有行列式为1的2×2矩阵所组成的群。

In mathematics, more specifically in the area of modern algebra known as group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group has no nontrivial abelian quotients (equivalently, its abelianization, which is the universal abelian quotient, is trivial). In symbols, a perfect group is one such that G = G (the commutator subgroup equals the group), or equivalently one such that G = {1} (its abelianization is trivial).