Abelian Groups
An arithmetic operation is said to be commutative if the order of its arguments is insignificant. With ordinary numbers, addition and multiplication are commutative operations; for example, 2 9 = 9 2 and 2 + 9 = 9 + 2. However, subtraction and division are not commutative since 2 - 9 < 9 - 2 and 2 / 9 < 9 / 2.
A group is called abelian if its main operation is commutative. Thus an additive group is abelian if a + b = b + a for all elements a, b in the group. A multiplicative group is abelian if a b = b a for all elements a, b in the group. The additive group Zn and the multiplicative group Zp* are both abelian groups.
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