query: Find subgroup of $S_5$ isomorphic to the quaternion $Q$
positive_passages.docid: 157853
positive_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: 58135
negative_passages.text: Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$
negative_passages.docid: 29453
negative_passages.text: An epimorphism from $S_{4}$ to $S_{3}$ having the kernel isomorphic to Klein four-group
negative_passages.docid: 141265
negative_passages.text: Finding a normal and not normal subgroup of $S_3$
negative_passages.docid: 149294
negative_passages.text: How do i prove how $S_5$ is generated by a two cycle and a five cycle?
negative_passages.docid: 11665
negative_passages.text: Show that $D_{12}$ is isomorphic to $D_6\times C_2$
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 128096
negative_passages.text: Let V denote the Klein 4-group. Show that $\text{Aut} (V)$ is isomorphic to $S_3$
negative_passages.docid: 151862
negative_passages.text: Is any subgroup of a direct product isomorphic to a direct product of subgroups?
negative_passages.docid: 85299
negative_passages.text: computing the orbits for a group action
negative_passages.docid: 76035
negative_passages.text: semi direct of quaternionic group
negative_passages.docid: 45627
negative_passages.text: Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
negative_passages.docid: 71245
negative_passages.text: $2 \times 2 $ Orthogonal Group
negative_passages.docid: 77221
negative_passages.text: Prove that $G$ has a subgroup isomorphic to $G/H$.
negative_passages.docid: 99382
negative_passages.text: What is needed to make Euclidean spaces isomorphic as groups?
negative_passages.docid: 87766
negative_passages.text: Using Cayley's Theorem to find an isomorphic subgroup.
negative_passages.docid: 145000
negative_passages.text: Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this?