query: Finding a subgroup $H$ of $G$ where, for some $a \in G$, $aha^{-1} \in H$ but $a^{-1}ha \notin H$ (for all $h \in H$)
positive_passages.docid: 41085
positive_passages.text: Conjugate subgroup strictly contained in the initial subgroup?
negative_passages.docid: 151130
negative_passages.text: When is the product of $n$ subgroups a subgroup?
negative_passages.docid: 8066
negative_passages.text: Sort-of-simple non-Hopfian groups
negative_passages.docid: 87766
negative_passages.text: Using Cayley's Theorem to find an isomorphic subgroup.
negative_passages.docid: 79826
negative_passages.text: $gHg^{-1}\subset H$ whenever $Ha\not = Hb$ implies $aH\not =bH$
negative_passages.docid: 71035
negative_passages.text: Non abelian subgroup of a abelian group.
negative_passages.docid: 103423
negative_passages.text: Normal subgroup where G has order prime
negative_passages.docid: 14301
negative_passages.text: Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
negative_passages.docid: 34724
negative_passages.text: For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
negative_passages.docid: 150042
negative_passages.text: Prove $x^{-1}Hx$ is a subgroup of $G$
negative_passages.docid: 39938
negative_passages.text: Subgroups of a cyclic group and their order.
negative_passages.docid: 91874
negative_passages.text: Existence of finite indexed normal subgroup for a given finite indexed subgroup.
negative_passages.docid: 128834
negative_passages.text: Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
negative_passages.docid: 19229
negative_passages.text: How to find all groups that have exactly 3 subgroups?
negative_passages.docid: 111024
negative_passages.text: Does $gHg^{-1}\subseteq H$ imply $gHg^{-1}= H$?
negative_passages.docid: 99630
negative_passages.text: For every $g\in G$ there exists an $h\in G$ such that $g = h^3$
negative_passages.docid: 116786
negative_passages.text: normal subgroups of Alternating group