query: If every proper subgroup of a group is finite, does it follow that the group is finite?
positive_passages.docid: 47539
positive_passages.text: Find an abelian infinite group such that every proper subgroup is finite
negative_passages.docid: 157819
negative_passages.text: Every group of order $56$ has a proper non - trivial normal subgroup?
negative_passages.docid: 88344
negative_passages.text: Order of a group and subsequent subgroups
negative_passages.docid: 112993
negative_passages.text: Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
negative_passages.docid: 113925
negative_passages.text: Normal Subgroup Counterexample
negative_passages.docid: 64269
negative_passages.text: Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
negative_passages.docid: 58937
negative_passages.text: Finite Index of Subgroup of Subgroup
negative_passages.docid: 49338
negative_passages.text: Is every group a Galois group?
negative_passages.docid: 151130
negative_passages.text: When is the product of $n$ subgroups a subgroup?
negative_passages.docid: 133954
negative_passages.text: Does every infinite group have a maximal subgroup?
negative_passages.docid: 72991
negative_passages.text: Is every group the automorphism group of a group?
negative_passages.docid: 97928
negative_passages.text: Normal subgroup of a normal subgroup
negative_passages.docid: 128300
negative_passages.text: Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
negative_passages.docid: 40846
negative_passages.text: When can a (finite) group be written as the quotient of some other group by its center?
negative_passages.docid: 42449
negative_passages.text: Is there any efficient algorithm for finding subgroups of a given finite group?
negative_passages.docid: 151727
negative_passages.text: If $|G/H|=4$ then $G$ is union of three proper subgroups
negative_passages.docid: 39976
negative_passages.text: If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?