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

1. ## [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.

Thanks in advance.

2. 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.

Thanks in advance.
< (1 2 3 4) > and Klein four-group.

3. 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.

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