Hi, I am told to give the subgroup H=<α,β> with α,β\inS3
α = (1 2)
β = (2 3)
So I know that H={αkβj|j,k\in(the integers)}
However, would αβα or βαβ (in this case, they're equal) be in H?
The set H={ε,(1 2), (2 3), (1 2 3), (1 3 2)} (or {ε,α,β,αβ,βα})
would not be closed because (1 2...