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Math Help - proofs

  1. #1
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    proofs

    I need help solving these proofs:

    Let G have order 4. Either G is cyclic, or every element of G is its own inverse. Conclude (but explain why) that every group of order 4 is abelian.

    If G has an element of order p and an element of order q, where p and q are distinct primes, then the order of G is a multiple of pq.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by steph615 View Post
    I need help solving these proofs:

    Let G have order 4. Either G is cyclic, or every element of G is its own inverse. Conclude (but explain why) that every group of order 4 is abelian.
    If G is cyclic then you are done. Cyclic groups are easily proven to be abelian.

    If G is not cyclic, then every element is its own inverse. So then ba = (ba)^{-1} = a^{-1}b^{-1} = ab.

    I'll let you formalize these statements in to a proof.

    -Dan
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