query: Commutator subgroup is the minimal normal subgroup such that quotient group is abelian
positive_passages.docid: 58307
positive_passages.text: Commutator Subgroup and the Largest Abelian Quotient
negative_passages.docid: 105322
negative_passages.text: Computing the quotient of SL(2,Z) by its commutator subgroup
negative_passages.docid: 43783
negative_passages.text: Abelian group (Commutative group)
negative_passages.docid: 85508
negative_passages.text: Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
negative_passages.docid: 116125
negative_passages.text: A group $G$ with $G'$ abelian and every abelian normal subgroup finite
negative_passages.docid: 3456
negative_passages.text: Commutator of two normal subgroups with trivial intersections
negative_passages.docid: 60208
negative_passages.text: Proof of property of abelian group
negative_passages.docid: 4883
negative_passages.text: Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
negative_passages.docid: 18415
negative_passages.text: Direct sum of Abelian groups and Isomorphism
negative_passages.docid: 51352
negative_passages.text: Subgroups of a finite abelian group
negative_passages.docid: 112677
negative_passages.text: understanding the commutator of dihedral group
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: 11043
negative_passages.text: A normal subgroup is the union of conjugacy classes.
negative_passages.docid: 97928
negative_passages.text: Normal subgroup of 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: 144988
negative_passages.text: Commutator Subgroup of Direct Product equals the Direct Product of the Commutator Subgroups
negative_passages.docid: 28108
negative_passages.text: Proving the kernel is a normal subgroup.