If teo subgroups are cyclic, the groups is cyclic?

Question

i've got a group $G$, and its subgroup $L$, L is normal in G. If L and G/L are cyclic, is G cyclic?

I know that in the other direction is true but what about this? i have no idea

Let $G$ be the non-cyclic group of order $4$ and let $L$ be a subgroup of order $2$. — lulu, May 22 '20 at 14:26
Of what? A single counterexample suffices to disprove a proposed theorem. — lulu, May 22 '20 at 14:28

score 1 · Accepted Answer · answered May 22 '20 at 14:28

1

Not necessarily. Think about S3, order 6, non-abelian.

answered May 22 '20 at 14:28

Prime Mover

1 Answers1