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Thread: Proving a set of permutations is a group

  1. #1
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    Proving a set of permutations is a group

    Hey there,

    I'm trying to prove a set of permutations is a group, but the textbook isn't very clear how to do so.

    G={id, (1 2), (1 3), (1 4)}; operation in S_4

    If anyone can offer any words of advice, that would be much appreciated.
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by manygrams View Post
    Hey there,

    I'm trying to prove a set of permutations is a group, but the textbook isn't very clear how to do so.

    G={id, (1 2), (1 3), (1 4)}; operation in S_4

    If anyone can offer any words of advice, that would be much appreciated.
    the product of $\displaystyle (1\,2)$ and $\displaystyle (1\,3)$ is $\displaystyle (1\,3\,2)$. this does not lie in $\displaystyle G$.Hence $\displaystyle G$ is not closed under multiplication. How can $\displaystyle G$ be a group?
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