I am having trouble with finding all of the elements of S_4 using cyclic notation.

I know there are 24 elements because 4!=24, but how do I find the elements.

Please help.

Printable View

- Oct 13th 2008, 06:26 AMmandy123find the elements of S_4
I am having trouble with finding all of the elements of S_4 using cyclic notation.

I know there are 24 elements because 4!=24, but how do I find the elements.

Please help. - Oct 13th 2008, 07:18 AMThePerfectHacker
Any element is a product of disjoint cycles.

Now find all the different possibilities.

**Identity (1)**: $\displaystyle \text{id}$

**2-cycles (6)**: $\displaystyle (12),(13),(14),(23),(24),(34)$

**3-cycles (8)**: $\displaystyle (123),(124),(132),(134),(142),(143),(234),(243)$

**4-cycles (6)**: $\displaystyle (1234),(1243),(1324),(1342),(1423),(1432)$

**2-cycles times 2-cycles (3)**: $\displaystyle (12)(34),(13)(24),(14)(23)$ - Oct 13th 2008, 10:23 AMmandy123
Oh I get it now!

Thank you so much!