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Math Help - Subgroups

  1. #1
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    Subgroups

    Hello all. Could you please help me to determine whether or not these are subgroups. Thanks, James

    G:=\Sigma_4, S=\left\{(a b)(c d)\right\} where the elements a,b,c,d are 1,2,3,4 (in any order, though must be distinct)

    G:=\Sigma_5, S=\left\{(a b)(c d)\right\} where the elements a,b,c,d are 1,2,3,4,5 (in any order, though must be distinct)
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  2. #2
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    Quote Originally Posted by alittletouched View Post
    Hello all. Could you please help me to determine whether or not these are subgroups. Thanks, James

    G:=\Sigma_4, S=\left\{(a b)(c d)\right\} where the elements a,b,c,d are 1,2,3,4 (in any order, though must be distinct)

    G:=\Sigma_5, S=\left\{(a b)(c d)\right\} where the elements a,b,c,d are 1,2,3,4,5 (in any order, though must be distinct)
    Basically all you need to show is if x,y\in S then xy\in S.
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