A group is a set with an operation defined on members of that set. The operation must meet the requirements of closure, associativity, identity and invertibility.
Example: the set of real numbers under addition is a group since:
A commutative group is a group where the operation is also commutative. If, for any members of the group S, a and b, a * b = b * a, then group S is a commutative group. Commutative groups are also called Abelian groups.
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