Hw7 Problem 6

In $S_{4}$, find a cyclic subgroup of order $4$ and a noncyclic subgroup of order $4$.
The subgroup generated by $(1234)$ is cyclic. $\langle (1234) \rangle = \{(1), (1234), (13)(24), (1432) \}$.
A noncyclic subgroup of order 4 in $S_{4}$ is $\{ (1), (12)(34), (13)(24), (14)(23) \}$.