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Thread: abtract algebra

  1. #1
    Mel
    Mel is offline
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    Exclamation abtract algebra

    If [tex]f\inS_3[\math], show that [tex]f^6=\iota[\math].

    Bear with me, I am still learning Latex.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mel View Post
    If $\displaystyle f \in S_3$, show that $\displaystyle f^6=\iota$.

    Bear with me, I am still learning Latex.
    use the $\displaystyle \Sigma$ button to input the [tex] tags correctly. you type the wrong slashes

    i am pretty sure there is a theorem to this effect. but note that 6 is the LCM of the orders of all the elements of $\displaystyle S_3$. it follows that any element raised to it will give the identity.

    you can look up the theorem to prove this elegantly, or since $\displaystyle S_3$ is small. just prove it by cases. $\displaystyle S_3$ has elements of orders 1,2, and 3. show that for each of these kinds of elements, the 6th power yields the identity
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