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Math Help - [SOLVED] N,M normal, (N n M) = {e}, then nm = mn

  1. #1
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    [SOLVED] N,M normal, (N n M) = {e}, then nm = mn



    Is this correct? I'm pretty sure it is, but the question was "starred," so I want to make sure its not much harder than I think it is.

    Thanks!
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    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by davismj View Post
    Is this correct? I'm pretty sure it is, but the question was "starred," so I want to make sure its not much harder than I think it is.

    Thanks!
    Please take the time to learn some LaTeX so we can help you better.

    It's not correct; how do you justify the step (nN\cap nM)m=m(nN\cap nM)?

    Let C=m^{-1}n^{-1}mn. Then C = (m^{-1}n^{-1}m)n \in N, and C=m^{-1}(n^{-1}mn) \in M. Therefore C=1, i.e. mn=nm.
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  3. #3
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    Quote Originally Posted by Bruno J. View Post
    Please take the time to learn some LaTeX so we can help you better.

    It's not correct; how do you justify the step (nN\cap nM)m=m(nN\cap nM)?

    Let C=m^{-1}n^{-1}mn. Then C = (m^{-1}n^{-1}m)n \in N, and C=m^{-1}(n^{-1}mn) \in M. Therefore C=1, i.e. mn=nm.
    Ah. Yea, my mistake was pretty stupid.

    I see what you did. Thanks very much!
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