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Math Help - Normal and Quotient groups

  1. #1
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    Normal and Quotient groups

    Let G be a group
    H be a subgroup of G

    G|H be set of all right cosets of H in G

    Is it correct to say H is normal sub-group of G, IFF (IF AND ONLY IF) G|H is a group?

    Thanks,
    Aman
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  2. #2
    MHF Contributor

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    Quote Originally Posted by aman_cc View Post
    Let G be a group
    H be a subgroup of G

    G|H be set of all right cosets of H in G

    Is it correct to say H is normal sub-group of G, IFF (IF AND ONLY IF) G|H is a group?

    Thanks,
    Aman
    one side is probably in your textbook. the other side: if G/H is a group, then f: G \longrightarrow G/H defined by f(g)=Hg is a well-defined group homomorphism and \ker f = H. thus H \lhd G.
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