query: Normal subgroup in a $p$-group
positive_passages.docid: 19720
positive_passages.text: A normal subgroup intersects the center of the $p$-group nontrivially
negative_passages.docid: 142413
negative_passages.text: Normal Subgroups of $SU(n)$
negative_passages.docid: 16804
negative_passages.text: Prove whether or not a subgroup is normal in the dihedral group $D_4$
negative_passages.docid: 7108
negative_passages.text: Normal subgroup of prime index
negative_passages.docid: 34552
negative_passages.text: Proper subgroups of non-cyclic p-group cannot be all cyclic?
negative_passages.docid: 58251
negative_passages.text: To show every sylow p-subgroup is normal in G
negative_passages.docid: 15630
negative_passages.text: Normal subgroup of prime order is characteristic
negative_passages.docid: 141043
negative_passages.text: $H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
negative_passages.docid: 106779
negative_passages.text: How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
negative_passages.docid: 76962
negative_passages.text: Sylow $p$-subgroups of $GL_n(\mathbb{F}_p)$
negative_passages.docid: 116125
negative_passages.text: A group $G$ with $G'$ abelian and every abelian normal subgroup finite
negative_passages.docid: 6134
negative_passages.text: Some Subgroup of Dihedral Group is Normal
negative_passages.docid: 43651
negative_passages.text: Normal subgroups and factor groups
negative_passages.docid: 44165
negative_passages.text: the image of normal subgroups
negative_passages.docid: 22444
negative_passages.text: Normal subgroups of dihedral groups
negative_passages.docid: 113357
negative_passages.text: Groups of order $pqr$ and their normal subgroups
negative_passages.docid: 44152
negative_passages.text: If $G$ has only one subgroup of order $n$, then that Subgroup is Normal