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Math Help - [SOLVED] Non-Commutative Groups

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    [SOLVED] Non-Commutative Groups

    Just a quick curiosity question, since I spent the afternoon building group multiplication tables. (I'm reviewing a bit for a new book I bought.)

    What is the smallest group that is non-commutative? I'm driving myself out of my mind trying to construct small (that is to say sets of less than 8 elements) non-commutative groups.

    Thanks!
    -Dan
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    Quote Originally Posted by topsquark View Post
    Just a quick curiosity question, since I spent the afternoon building group multiplication tables. (I'm reviewing a bit for a new book I bought.)

    What is the smallest group that is non-commutative? I'm driving myself out of my mind trying to construct small (that is to say sets of less than 8 elements) non-commutative groups.

    Thanks!
    -Dan
    The symettric group on {1,2,3}. It has 3! = 6 elements.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    The symettric group on {1,2,3}. It has 3! = 6 elements.
    A non-commutative symmetric group? Man I really DO need a review. I was thinking symmetric groups had to be commutative.

    Well, at least I have a good place to start tomorrow morning!

    Thanks.
    -Dan
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    Quote Originally Posted by topsquark View Post
    I was thinking symmetric groups had to be commutative.
    I wish! Then all of group theory would be so easy.
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