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# Symmetric Group, Permutations

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For any set the bijections from onto together with the composition of mappings as operation form a group, the so called symmetric group of .

If , then this group is called the symmetric group of degree (notation: ). The elements of are called permutations. has elements. A permutation can be written as:

The group of permutations is in general not commutative, as shown in the example:

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