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Math Help - Centerlizer

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by PookieLemma View Post
    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.
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  3. #3
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    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
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