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Thread: Group proof

  1. #1
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    Group proof

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

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

    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 $\displaystyle i)\Rightarrow ii)$, $\displaystyle ii)\Rightarrow iii)$ and $\displaystyle iii)\Rightarrow i)$.
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