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Math Help - Sylow's theorem

  1. #1
    Newbie dangkhoa's Avatar
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    Sylow's theorem

    Let G be a group of order pq where p and q are distinct primes. Prove
    that G is soluble.

    Can you give me some instructions on this question by using Sylow's theorem please?


    Many thanks
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  2. #2
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    Quote Originally Posted by dangkhoa View Post
    Let G be a group of order pq where p and q are distinct primes. Prove
    that G is soluble.

    Can you give me some instructions on this question by using Sylow's theorem please?


    Many thanks

    If p=q the group is abelian, otherwise suppose p>q\Longrightarrow there exists a normal Sylow p-subgroup. and then 1\leq P\leq G is an abelian series for G.

    Tonio
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