query: Index and Normal Subgroups?
positive_passages.docid: 75568
positive_passages.text: Subgroup of index $2$ is Normal
negative_passages.docid: 28108
negative_passages.text: Proving the kernel is a normal subgroup.
negative_passages.docid: 156247
negative_passages.text: Question about permutations and cycles (Groups and Symmetries)
negative_passages.docid: 91874
negative_passages.text: Existence of finite indexed normal subgroup for a given finite indexed subgroup.
negative_passages.docid: 23941
negative_passages.text: Normal Subgroups that Intersect Trivially
negative_passages.docid: 99114
negative_passages.text: Subgroups of index 3 are normal
negative_passages.docid: 123610
negative_passages.text: How to show that the commutator subgroup is a normal subgroup
negative_passages.docid: 11731
negative_passages.text: Normal subgroups of $S_4$
negative_passages.docid: 125244
negative_passages.text: Equivalent definitions of normal subgroups
negative_passages.docid: 116125
negative_passages.text: A group $G$ with $G'$ abelian and every abelian normal subgroup finite
negative_passages.docid: 44165
negative_passages.text: the image of normal subgroups
negative_passages.docid: 103002
negative_passages.text: Group equals union of two subgroups
negative_passages.docid: 135341
negative_passages.text: number theory about index
negative_passages.docid: 99999
negative_passages.text: A question on identifying normal subgroups of $S_4$
negative_passages.docid: 45580
negative_passages.text: Intersection of conjugate subgroups is normal
negative_passages.docid: 23533
negative_passages.text: All subgroups normal $\implies$ abelian group
negative_passages.docid: 86336
negative_passages.text: For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists