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Math Help - Order of element

  1. #1
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    Order of element

    Let H be a group in which h=I for all h is an element of H.
    Prove: Suppose |H|<∞. Let {h₁,h₂,..hn} be minimal set of generators for H. then
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  2. #2
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    Quote Originally Posted by apple2009 View Post
    Let H be a group in which h=I for all h is an element of H.
    Prove: Suppose |H|<∞. Let {h₁,h₂,..hn} be minimal set of generators for H. then

    Any element is a product of h_1,...,h_n and since H is abelian (why?) we can even order that product in ascending index order:
    h_1^{\epsilon_1}\cdot...\cdot h_n^{\epsilon_n}\,,\,\,with\,\,\,\epsilon_i=0\,\,o  r\,\, 1
    Well, in how many ways can you choose the first factor in such a product? In how many the second factor?....

    Tonio
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