abtract algebra

Mel · #1 $Old$ September 28th, 2008, 08:21 PM

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

Bear with me, I am still learning Latex.

Jhevon · #2 $Old$ September 28th, 2008, 08:31 PM

Quote:

Originally Posted by Mel $View Post$

If $f \in S_3$ , show that $f^6=\iota$ .

Bear with me, I am still learning Latex.

use the $\Sigma$ button to input the [math] 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 $S_3$ . it follows that any element raised to it will give the identity.

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