Generators and Relations
The symmetric group on n-letters, Sn, may be described as follows. It has generators: and relations:
One thinks of as swapping the i-th and i+1-st position.
Other popular generating sets include the set of transpositions that swap 1 and i for 2 ≤ i ≤ n and a set containing any n-cycle and a 2-cycle of adjacent elements in the n-cycle.
Read more about this topic: Symmetric Group
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