“Abelian” in this context means “commutative”. That is, if you have some operator * then it is abelian if a * b = b * a for all a and b in the domain of *. If that id not the case it is “non-abelian”.
The name “Abelian” is after Nils Henrik Abel, one of the founders of abstract algebra who died tragically young of tuberculosis brought on by extreme poverty.
The name “Abelian” is after Nils Henrik Abel, one of the founders of abstract algebra who died tragically young of tuberculosis brought on by extreme poverty.