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Is there an infinite finitely generated (non-cyclic) $p$-group $G$ such that the intersection of all nontrivial subgroups of $G$ is a nontrivial subgroup?

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An example is given here. And here are some more words to make MO happy.

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  • $\begingroup$ thanks. there's a simple workaround for leaving MO unhappy, $\endgroup$ – nano - merge me Jul 27 '14 at 7:39

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