What does the term abelian mean?

Answer 1

The term abelian is most commonly encountered in group theory, where it refers to a specific type of group known as an abelian group. An abelian group, simply put, is a commutative group, meaning that when the group operation is applied to two elements of the group, the order of the elements doesn't matter.

For example:

Let G be a group with multiplication * or addition +. If, for any two elements a, b Є G, a*b = b*a or a + b = b + a, then we call the group abelian.

There are other uses of the term abelian in other fields of math, and most of the time, the idea of commutativity is involved.

The term is named after the mathematician, Niels Abel.

Answer 2

a group or set of group is said to be abelian if the law of commutation is always held.

it means if for a group or set S having elements a,b belongs to S then a*b=b*a

then the group is called abelian group.