The symmetric group on n-letters, Sn, may be described as follows.
σi is the permutation that swaps the i:th element with the i+1 one.
With the generators: σ1, . . ., σn-1
And the following relations:
- (σi)(σj+1)(σi) =(σj+1)(σi)(σj+1) ∀ i
- σij = σjσi if |i - j| ≥ 2
- (σi)² = 1
How do I verify the above for the two simplest cases where n = 2 and where n = 3?
Can somebody help me out? I don't want anyone to solve this for me but rather if someone just could give me a hint and a push in the right direction.