# [SOLVED] Cylic and a non cyclic subgroup in the Permutation group S(4)

• April 12th 2009, 09:31 PM
akolman
[SOLVED] Cylic and a non cyclic subgroup in the Permutation group S(4)
I am stuck with this problem.

In $S_4$, find a cyclic subgroup of order 4 and a noncyclic subgroup of order 4.

• April 13th 2009, 12:00 AM
NonCommAlg
Quote:

Originally Posted by akolman
I am stuck with this problem.

In $S_4$, find a cyclic subgroup of order 4 and a noncyclic subgroup of order 4.

< (1 2 3 4) > and Klein four-group.
• April 13th 2009, 10:30 AM
ThePerfectHacker
Quote:

Originally Posted by akolman
I am stuck with this problem.

In $S_4$, find a cyclic subgroup of order 4 and a noncyclic subgroup of order 4.

For non-cyclic take $V=\{ (12)(34),(13)(24),(14)(23), \text{id} \}$.