I am trying to find all 3-Sylows of $A_{4}$. By definition, all of them have order 3. Now the question is how to find all permutations of order 3. Now, every permutation can be written as the product of disjoint cycles. Moreover, the order of the product is the lcm of the order of the cycles. Can I conclude from these two facts that the only elements in $S_{n}$ of order 3 are of the form (a b c)?
2026-03-28 12:34:08.1774701248
all permutations of order 3
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