query: Describe all groups which contain no proper subgroup.
positive_passages.docid: 22301
positive_passages.text: If $G$ has no proper subgroup, then $G$ is cyclic of prime order
negative_passages.docid: 43832
negative_passages.text: Which groups are derived subgroups?
negative_passages.docid: 47539
negative_passages.text: Find an abelian infinite group such that every proper subgroup is finite
negative_passages.docid: 68672
negative_passages.text: Commutator subgroup of rank-2 free group is not finitely generated.
negative_passages.docid: 115574
negative_passages.text: Finitely presented group with fewer relations than generators.
negative_passages.docid: 141379
negative_passages.text: All groups where underlying set has at most 4 elements
negative_passages.docid: 2254
negative_passages.text: Finite group with isomorphic normal subgroups and non-isomorphic quotients?
negative_passages.docid: 152904
negative_passages.text: Groups with Same Number Of Elements and Subgroups
negative_passages.docid: 156549
negative_passages.text: Prove that there is no group $G$ s.t. $\operatorname{Aut}(G)=\mathbb{Q}$
negative_passages.docid: 23941
negative_passages.text: Normal Subgroups that Intersect Trivially
negative_passages.docid: 10602
negative_passages.text: Monotone Union of subgroups being subgroup
negative_passages.docid: 151210
negative_passages.text: How can we find and categorize the subgroups of $\mathbb{R}$?
negative_passages.docid: 19229
negative_passages.text: How to find all groups that have exactly 3 subgroups?
negative_passages.docid: 111141
negative_passages.text: Why is every discrete subgroup of a Hausdorff group closed?
negative_passages.docid: 78048
negative_passages.text: Group of order 24 with no element of order 6 is isomorphic to $S_4$
negative_passages.docid: 91772
negative_passages.text: Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
negative_passages.docid: 102912
negative_passages.text: Subgroups of finitely generated groups are not necessarily finitely generated