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Math Help - Prove Abelian group

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    Prove Abelian group

    If G is an abelian group and the group G' is a homomorphic image of G, prove that G' is abelian.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rainyice View Post
    If G is an abelian group and the group G' is a homomorphic image of G, prove that G' is abelian.
    I just helped someone with this in another thread.

    Just note that if a,b\in G' then a=\theta(g),b=\theta(g') and so ab=\theta(g)\theta(g')=\theta(gg')=\theta(g'g)=\th  eta(g')\theta(g)=ba
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    Quote Originally Posted by Drexel28 View Post
    I just helped someone with this in another thread.

    Just note that if a,b\in G' then a=\theta(g),b=\theta(g') and so ab=\theta(g)\theta(g')=\theta(gg')=\theta(g'g)=\th  eta(g')\theta(g)=ba
    do you mind linking me to that thread? thank you ~!
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rainyice View Post
    do you mind linking me to that thread? thank you ~!
    I said less there than I did here, so I don't think it would help.
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