query: Why Quotient group is not a subgroup?
positive_passages.docid: 153797
positive_passages.text: Is a quotient group a subgroup?
negative_passages.docid: 66863
negative_passages.text: How is the quotient group related to the direct product group?
negative_passages.docid: 59902
negative_passages.text: Example of $2$ non-isomorphic groups that have the same quotients
negative_passages.docid: 70298
negative_passages.text: Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
negative_passages.docid: 97565
negative_passages.text: Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
negative_passages.docid: 99788
negative_passages.text: Why does a multiplicative subgroup of a field have to be cyclic?
negative_passages.docid: 2761
negative_passages.text: If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
negative_passages.docid: 18182
negative_passages.text: An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
negative_passages.docid: 46904
negative_passages.text: Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
negative_passages.docid: 27703
negative_passages.text: an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
negative_passages.docid: 14947
negative_passages.text: Who named "Quotient groups"?
negative_passages.docid: 11825
negative_passages.text: Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \in H \iff a \in H\}$. Prove that $K$ is a subgroup of $G$.
negative_passages.docid: 149772
negative_passages.text: How can a Lie subgroup of a matrix Lie group not be a matrix Lie group
negative_passages.docid: 148369
negative_passages.text: Quotient groups of D10
negative_passages.docid: 113413
negative_passages.text: How do I show that two groups are not isomorphic?
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: 2458
negative_passages.text: Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?