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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Originally Posted by apple2009 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: is a subgroup of . Now apply Lagrange's theorem.
am I need to prove v is a subgroup of G? and how?
Originally Posted by apple2009 am I need to prove v is a subgroup of G? and how? You already know that is a subgroup of (or you should). Now use the fact that and Lagranges theorem.
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