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Math Help - subgroup generated

  1. #1
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    subgroup generated

    Let S be a proper subgroup of G. If G-S is the complement of S, prove that <G-S>=G.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Biscaim View Post

    Let S be a proper subgroup of G. If G-S is the complement of S, prove that <G-S>=G.

    Thanks in advance.
    clearly <G-S> \subseteq G. now let g \in G. if g \in G - S, then g \in <G-S>. if g \in S, then choose x \in G-S. then x^{-1} \in G-S and gx=y \in G-S. so: g=yx^{-1} \in <G-S>. Q.E.D.
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