# Math Help - Centerlizer

1. ## Centerlizer

Let a, b, g $\in G$ , if ab $\in$ C then a,b $\in G$.

If ab $\in C_g$ then ba $\in C_g$

I am getting lost.

2. Originally Posted by PookieLemma
Let a, b, g $\in G$ , if ab $\in$ C then a,b $\in G$.

If ab $\in C_g$ then ba $\in C_g$

I am getting lost.
This is not true, if you look here you will realize the centralizer is S3, which is a non-abelian group.

3. ## I was a bit unclear

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 $x \in G$ 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