In abstract algebra, an abelian group, an aa cried a commutative group, is a group in which the result o applyin the group operation tae twa group elements disna depend on the order in which thay are written. That is, thir are the groups that obey the axiom o commutativity. Abelian groups generalise the arithmetic o addeetion o integers. Thay are named efter Niels Henrik Abel.
The concept o an abelian group is ane o the first concepts encoontered in unnergraduate abstract algebra, frae which mony ither basic concepts, such as modules an vector spaces are developed. The theory o abelian groups is generally simpler than that o thair non-abelian coonterparts, an finite abelian groups are very well unnerstuid. On the ither haund, the theory o infinite abelian groups is an aurie o current resairch.
- Jacobson (2009), p. 41