query: Does there exist a group that can be covered by conjugates of its proper subgroup?
positive_passages.docid: 72150
positive_passages.text: Union of the conjugates of a proper subgroup
negative_passages.docid: 154398
negative_passages.text: Show that H is a subgroup of G
negative_passages.docid: 98474
negative_passages.text: Show the existence of a certain subgroup of F2
negative_passages.docid: 89382
negative_passages.text: In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
negative_passages.docid: 39938
negative_passages.text: Subgroups of a cyclic group and their order.
negative_passages.docid: 87766
negative_passages.text: Using Cayley's Theorem to find an isomorphic subgroup.
negative_passages.docid: 142421
negative_passages.text: Conjugacy Classes in Finite Groups
negative_passages.docid: 13059
negative_passages.text: If a group is the union of two subgroups, is one subgroup the group itself?
negative_passages.docid: 82843
negative_passages.text: Subgroups of $\Bbb{R}^n$ that are closed and discrete
negative_passages.docid: 23941
negative_passages.text: Normal Subgroups that Intersect Trivially
negative_passages.docid: 124237
negative_passages.text: Group equals union of three subgroups
negative_passages.docid: 8066
negative_passages.text: Sort-of-simple non-Hopfian groups
negative_passages.docid: 64582
negative_passages.text: Group covered by finitely many cosets
negative_passages.docid: 42582
negative_passages.text: Infinite group with only two conjugacy classes
negative_passages.docid: 113357
negative_passages.text: Groups of order $pqr$ and their normal subgroups
negative_passages.docid: 68955
negative_passages.text: Characterising subgroups of Prüfer $p$-groups.
negative_passages.docid: 91997
negative_passages.text: Product of two subgroups the whole group?