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Math Help - plz solve these problems.....

  1. #1
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    plz solve these problems.....

    1:Show that union of two subgroups may not be a group?

    2:If G is a group and H is a subgroup of index 2 in G,prove that H is normal subgroup of G?
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  2. #2
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    Quote Originally Posted by Mathventure View Post
    1:Show that union of two subgroups may not be a group?
    Take S_3 and <(12)> with <(13)>.

    2:If G is a group and H is a subgroup of index 2 in G,prove that H is normal subgroup of G?
    Let a\in G. If a\in H then aH=Ha. If a\not \in H then aH is the coset other than H, and Ha is the coset other than H. Since there are only two cosets it means aH=Ha. Thus, H is a normal subgroup of G.
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