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Math Help - Abstract Algebra: Lagrange's Theorem

  1. #1
    is up to his old tricks again! Jhevon's Avatar
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    Abstract Algebra: Lagrange's Theorem

    Hi all,

    Another problem I am not sure whether I am missing something or not.

    Problem:

    A finite group G has elements of orders p and q, where p and q are distinct primes. What can you conclude about |G|?


    Solution:

    I said that |G| = kpq for some k \in \mathbb{Z}_{>0} . As a consequence of Lagrange's Theorem (the orders of the elements must divide |G|)

    does that seem like the observation they wanted me to make?

    Thanks
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  2. #2
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    Consider \mathbb{Z}_{pq}, \mathbb{Z}_{2pq}, \mathbb{Z}_{3pq}, ... all of these groups have elements of orders p,q. While their orders are pq,2pq,3pq,.... Thus, it does not seem as there is a way to improve |G| = kpq, what your wrote.
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