I have this exercise:
Let $h=(12)(34)(56)$ belonging to $S_6$ and let $H=\langle h\rangle$ be the subgroup. Let $g=(123456)$
And then I have to find the pairs of inversions.
I understand inversions as those numbers that needs to be replaced to be in order. Since there is no numbers in $h# that are out of order, I would say there's no inversions.
However the solution says $I_h=\{(1,2),(3,4),(5,6)\}$
So I know I'm wrong 'cause obviously there are inversions. So how would I find the pairs of inversions instead?