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Math Help - Factor groups question

  1. #1
    DCU
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    Factor groups question

    Factor groups question-6z69g5.jpg
    Basically I know how to do the first part, it's just the multiplication table giving me problems. I know the headings for the table should be H, (1,2)H, (1,3)H, (2,3)H, (1,2,3)H, (1,3,2)H but I don't know anymore.
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  2. #2
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    Multiplication in factor groups is easy. It is defined as
    (aH)(bH) = abH.

    For example Let G=\mathbb{Z}, H = Z\mathbb{Z}. Since G is abelian, H is normal in G.

    Consider two cosets of 4\mathbb{Z}, (1+ 4\mathbb{Z}) +(2+4\mathbb{Z}) = (3 + 4\mathbb{Z}).

    Now in your example, we take [(12)H][(24)H] = (14)H. since (12)(24) = (14)
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