阿贝尔群(Abelian group)也称为交换群(commutative group)或可交换群，它是满足其元素的运算不依赖于它们的次序（交换律公理）的群。阿贝尔群推广了整数集合的加法运算。阿贝尔群以挪威数学家尼尔斯·阿贝尔命名。

阿贝尔群的概念是抽象代数的基本概念之一。其基本研究对象是模和矢量空间。阿贝尔群的理论比其他非阿贝尔群简单。有限阿贝尔群已经被彻底地研究了。无限阿贝尔群理论则是目前正在研究的领域。

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written (the axiom of commutativity). Abelian groups generalize the arithmetic of addition of integers. They are named after Niels Henrik Abel.