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Math Help - Abelian group

  1. #1
    Junior Member
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    Abelian group

    Hi people,

     (G;.) is a group.
    I must show that if  (\forall a;b \in G): (ab)^2=a^2b^2 \Longrightarrow (G;.) is abelian.

    Can you help me please???

    And thanks.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by bhitroofen01 View Post
    Hi people,

     (G;.) is a group.
    I must show that if  (\forall a;b \in G): (ab)^2=a^2b^2 \Longrightarrow (G;.) is abelian.

    Can you help me please???

    And thanks.
    ab=ababb^{-1}a^{-1}=(ab)^2b^{-1}a^{-1}=a^2b^2b^{-1}a^{-1}=a^2ba^{-1} thus multiplying both sides by a on the left gives aba=a^2b\implies ba=ab
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