query: Prove that no group $G$ satisfies $G/Z \approx Q_8$ where $Z$ is centre of $G$
positive_passages.docid: 41572
positive_passages.text: $G/Z$ cannot be isomorphic to quaternion group
negative_passages.docid: 124309
negative_passages.text: $g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
negative_passages.docid: 3203
negative_passages.text: Quotient group $\mathbb Z^n/\ \text{im}(A)$
negative_passages.docid: 59561
negative_passages.text: Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
negative_passages.docid: 48585
negative_passages.text: Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
negative_passages.docid: 121142
negative_passages.text: Take $G$ to be a group of order $600$. Prove that for any element a in $G$ there exist a $b$ in $G$ such that $a = b^7$
negative_passages.docid: 150585
negative_passages.text: Group with $a=a^{-1}$ for all $a\in G$ is abelian
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 40846
negative_passages.text: When can a (finite) group be written as the quotient of some other group by its center?
negative_passages.docid: 86336
negative_passages.text: For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
negative_passages.docid: 59041
negative_passages.text: Centre of $GL_n(\mathbb R)$
negative_passages.docid: 67383
negative_passages.text: Prove that $G'$ is not planar.
negative_passages.docid: 156319
negative_passages.text: Show that a group with $|G| = 33$ contains an element of order $3$
negative_passages.docid: 25832
negative_passages.text: Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
negative_passages.docid: 91774
negative_passages.text: Existence of group $G$ with $|G|>2$ and automorphism group of odd order
negative_passages.docid: 157853
negative_passages.text: $Q_8$ is isomorphic to a subgroup of $S_8$, but not isomorphic to a subgroup of $S_n$ for $n\leq 7$.
negative_passages.docid: 80849
negative_passages.text: There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)