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Math Help - Order of element

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    Order of element

    Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by apple2009 View Post
    Let G be a finite group. Prove the order of any element v (which v is an element of G) divides the order |G|of G.
    Hint: \langle v\rangle is a subgroup of G. Now apply Lagrange's theorem.
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    am I need to prove v is a subgroup of G? and how?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by apple2009 View Post
    am I need to prove v is a subgroup of G? and how?
    You already know that \langle v\rangle is a subgroup of G (or you should). Now use the fact that |v|=|\langle v\rangle| and Lagranges theorem.
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