query: Show that $H$ is a normal subgroup of $G$?
positive_passages.docid: 55493
positive_passages.text: Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
negative_passages.docid: 70373
negative_passages.text: Intersection of normal subgroups proof
negative_passages.docid: 107935
negative_passages.text: If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
negative_passages.docid: 71819
negative_passages.text: Prove that $H$ is normal.
negative_passages.docid: 37379
negative_passages.text: Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$.
negative_passages.docid: 54911
negative_passages.text: The preimage of a normal subgroup under a group homomorphism is normal
negative_passages.docid: 2174
negative_passages.text: Proving that HK is a subgroup when K is normal
negative_passages.docid: 102622
negative_passages.text: K is a subgroup of G. Show that K is not a normal subgroup
negative_passages.docid: 44934
negative_passages.text: Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
negative_passages.docid: 36040
negative_passages.text: A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
negative_passages.docid: 11957
negative_passages.text: G is the product of its Sylow subgroups
negative_passages.docid: 142894
negative_passages.text: Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
negative_passages.docid: 14255
negative_passages.text: Commutator subgroup and cyclic normal subgroup
negative_passages.docid: 45727
negative_passages.text: If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
negative_passages.docid: 80186
negative_passages.text: How to show that $K\leq S_4$ is a normal subgroup?
negative_passages.docid: 51359
negative_passages.text: Prove that every subgroup of an abelian group is a normal subgroup.
negative_passages.docid: 77221
negative_passages.text: Prove that $G$ has a subgroup isomorphic to $G/H$.