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A group is a set together with an operation (called the group law of ) that combines any two elements and to form another element, denoted or . To qualify as a group, the set and operation must satisfy four requirements known as the group axioms: closure, associativity, identity element, and inverse element. If for all and in , then the group is commutative (or abelian).

In this Demonstration, the group law is the composition of permutations of the set . For example, .