# find the elements of S_4

• Oct 13th 2008, 06:26 AM
mandy123
find 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.

• Oct 13th 2008, 07:18 AM
ThePerfectHacker
Quote:

Originally Posted by mandy123
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.

Any element is a product of disjoint cycles.
Now find all the different possibilities.

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

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

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

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

2-cycles times 2-cycles (3): $(12)(34),(13)(24),(14)(23)$
• Oct 13th 2008, 10:23 AM
mandy123
Oh I get it now!
Thank you so much!