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Existence of an infinite finitely generated non-cyclic $p$-group with nontrivial intersection of nontrivial subgroups

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

Existence of an infinite finitely generated non-cyclic $p$-group with nontrivial intersection of nontrivial subgroups

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?

Existence of an infinite finitely generated $p$-group with nontrivial intersection of nontrivial subgroups

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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Existence of an infinite finitely generated non-cyclic $p$-group with nontrivial intersection of nontrivial subgroups

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?

Existence of an infinite finitely generated $p$-group with nontrivial intersection of subgroups

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

Existence of an infinite finitely generated non-cyclic $p$-group with nontrivial intersection of nontrivial subgroups

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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Existence of an infinite finitely generated $p$-group with nontrivial intersection of subgroups

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