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.

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Famous quotes containing the word relations:

    “Children, who play life, discern its true law and relations more clearly than men, who fail to live it worthily, but who think that they are wiser by experience, that is, by failure.”
    —Henry David Thoreau (1817–1862)