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of) .

Definition and first properties

The symmetric group on a finite set is the group whose elements are all bijective functions from to and whose group operation is that of function composition. For finite sets, "permutations" and "bijective functions" refer to the same operation, namely rearrangement. The symmetric group of degree is the symmetric group on the set .

The symmetric group on a set is denoted in various ways, including , , , , and . If is the

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