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Math Help - Group proof

  1. #1
    MHF Contributor
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    Group proof

    G is a group and x,y\in G.

    Prove that xy=yx iff y^{-1}xy=x iff x^{-1}y^{-1}xy=1.

    How can I break this statement up to prove. With iff proofs, I know we go both directions but how is it broken up when another iff is embedded in it?
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  2. #2
    Super Member girdav's Avatar
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    Re: Group proof

    If we have to show that we have i) iff ii) iff iii), then just prove that i)\Rightarrow ii), ii)\Rightarrow iii) and iii)\Rightarrow i).
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