I have a review question which wants me to show equivalency between the two ends of the question, and I came to the conclusion one way top show it is abelian would be to prove it is a cyclic group, but I am currently stuck on if my idea is right/what to do next. Any help is greatly appreciated.
2026-04-01 23:32:22.1775086342
Does $H \unlhd G$ imply $G/H$ is cyclic and therefore abelian?
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The converse is true: if $G/H$ is a cyclic group, then $G$ is abelian.
If we take an abelian group $G$ and non-abelian group $H$, then $G \times H$ is not abelian, even though $(G, 1) \trianglelefteq G \times H$.