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Math Help - Show H∩N is a normal subgroup of H

  1. #1
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    Exclamation Show H∩N is a normal subgroup of H

    Hi everyone,

    the question is:

    If N is normal subgroup of G and H is any subgroup of G. Show H∩N is a normal subgroup of H.
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  2. #2
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    It is easy to check that he intersection of 2 subgroups is a subgroup (can you do this?)

    Now, let x\in H\cap N and g\in H. Then gxg^{-1}\in H because x and g are in H and H is a group. Also, gxg^{-1}\in N because N is normal in G.
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