Symmetric Group - Generators and Relations

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:

    “Happy will that house be in which the relations are formed from character; after the highest, and not after the lowest order; the house in which character marries, and not confusion and a miscellany of unavowable motives.”
    —Ralph Waldo Emerson (1803–1882)