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
Famous quotes containing the word relations:
“Our relations to each other are oblique and casual.”
—Ralph Waldo Emerson (1803–1882)