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Math Help - Centralizer

  1. #1
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    Centralizer

    Prove that C_G(A)=\{g\in G:g^{-1}ag=a, \forall a\in A\}

    Is this just asking me to prove g^{-1}ag iff ga = ag?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: Centralizer

    Quote Originally Posted by dwsmith View Post
    Prove that C_G(A)=\{g\in G:g^{-1}ag=a, \forall a\in A\}

    Is this just asking me to prove g^{-1}ag iff ga = ag?
    Presumably you are asked to prove that \left\{g\in G:ga=ag,\;\forall a\in A\right\}=\left\{g\in G:g^{-1}ag=a,\; \forall a\in A\right\}. Then, yes, it follows from the fact that ag=ga if and only if g^{-1}ag=a.
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