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For questions requesting examples of a certain structure or phenomenon

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Maximal subgroups of abelian groups and Q-algebras

Let $G$ be an abelian group which does not have a maximal subgroup. Does it follow that $G$ is a $\mathbb{Q}$-algebra? It is easy to see that $\mathbb{Q}$-algebras do not admit any maximal subgroups. …
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