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 thisforme but rather if someone just could give me a hint and a push in the right direction.