here you will realize the centralizer is S3, which is a non-abelian group.
I have two questions:
1) Let a, b, g , if ab C then a,b .
2) Let a, b, g , If ab then ba
1) Let then if ax=xa and same with b if 1 is true.
I get lost because I try to get ax=xa but I keep winding up with aba^-1 or some other conjugate and not ax=xa.
2) Similar issue here, I do I work this out because I keep getting conjugates