query: Why commutator subgroup is normal to G?
positive_passages.docid: 76317
positive_passages.text: Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
negative_passages.docid: 28108
negative_passages.text: Proving the kernel is a normal subgroup.
negative_passages.docid: 58694
negative_passages.text: Which non-abelian finite groups have the property that every subgroup is normal?
negative_passages.docid: 43651
negative_passages.text: Normal subgroups and factor groups
negative_passages.docid: 116936
negative_passages.text: Commutator subgroup and subgroup generated by square.
negative_passages.docid: 1220
negative_passages.text: Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
negative_passages.docid: 92493
negative_passages.text: If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
negative_passages.docid: 54911
negative_passages.text: The preimage of a normal subgroup under a group homomorphism is normal
negative_passages.docid: 55493
negative_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: 74411
negative_passages.text: Normalizer of Unipotent subgroup in General Linear group
negative_passages.docid: 102146
negative_passages.text: If a group mod its commutator subgroup is cyclic, then the group is abelian?
negative_passages.docid: 122970
negative_passages.text: A question on $p$-groups, and order of its commutator subgroup.
negative_passages.docid: 68436
negative_passages.text: Groups in derived series are normal in the whole group
negative_passages.docid: 88199
negative_passages.text: The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
negative_passages.docid: 113013
negative_passages.text: Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
negative_passages.docid: 58205
negative_passages.text: $ N $ normal in a finite group $ G $, $ |N| = 5 $ and $ |G| $ odd. Why is $ N \subseteq Z(G) $?
negative_passages.docid: 141043
negative_passages.text: $H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$