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

  • 2
    $\begingroup$ Let $G$ be the non-cyclic group of order $4$ and let $L$ be a subgroup of order $2$. $\endgroup$ – lulu May 22 at 14:26
  • $\begingroup$ i need the demostration $\endgroup$ – User160 May 22 at 14:27
  • 4
    $\begingroup$ Of what? A single counterexample suffices to disprove a proposed theorem. $\endgroup$ – lulu May 22 at 14:28

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

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