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Math Help - Normal subgroup

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    Junior Member mathemanyak's Avatar
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    Normal subgroup

    Let G be a group and let H<=G with [G:H]=2 show that H normal subgroup of G
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    Quote Originally Posted by mathemanyak View Post
    Let G be a group and let H<=G with [G:H]=2 show that H normal subgroup of G
    H is a normal subgroup if and only if aH=Ha. Create the cosets G/H. If a\in H then aH=Ha because G/H partitions the set G into two sets. If a\in G-H then aH\not = H and Ha\not = H thus aH=Ha again because G/H partitions the set into two sets.
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