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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- Sep 28th 2008, 07:21 PMMelabtract algebra
If [tex]f\inS_3[\math], show that [tex]f^6=\iota[\math].

Bear with me, I am still learning Latex. - Sep 28th 2008, 07:31 PMJhevon
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