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Math Help - "x is a conjugate of y"

  1. #1
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    "x is a conjugate of y"

    Prove that in any group, the relation "x is a conjugate of y" is an equivalence relation.

    Not sure what to do here
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by natmov85 View Post
    Prove that in any group, the relation "x is a conjugate of y" is an equivalence relation.

    Not sure what to do here
    I assume you are talking about conjugacy classes a\sim b\Leftrightarrow a=gbg^{-1},\text{ }g\in G.

    Reflexivity: try g=e

    Symmetry: Try switching g and g^{-1}

    Transitivity: This is up to you.
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