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:

    “Think of the many different relations of form and content. E.g., the many pairs of trousers and what’s in them.”
    —Mason Cooley (b. 1927)