query: Is $O(4)\cong SO(4)\times C_2$?
positive_passages.docid: 154754
positive_passages.text: Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?
negative_passages.docid: 157840
negative_passages.text: Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
negative_passages.docid: 99999
negative_passages.text: A question on identifying normal subgroups of $S_4$
negative_passages.docid: 125980
negative_passages.text: Isomorphic Lie Algebra $so(4)$ and $su(2) \times su(2)$
negative_passages.docid: 37351
negative_passages.text: Group of Order $p^2$ Isomorphic to $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_{p}$ $\times$ $\mathbb{Z}_{p}$
negative_passages.docid: 136756
negative_passages.text: Computational check whether $G\cong \tilde G$
negative_passages.docid: 95686
negative_passages.text: $Lie(G \times H)\cong Lie(G)\oplus Lie(H)$
negative_passages.docid: 81197
negative_passages.text: Why is $SO(3)\times SO(3)$ isomorphic to $SO(4)$?
negative_passages.docid: 114394
negative_passages.text: Determine whether $\mathbb{Z}\times \mathbb{Z}$ and $\mathbb{Z}\times \mathbb{Z}\times \mathbb{Z}$ are isomorphic groups or not.
negative_passages.docid: 2235
negative_passages.text: Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
negative_passages.docid: 43645
negative_passages.text: Show that $G/H\cong S_3$
negative_passages.docid: 35626
negative_passages.text: Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?
negative_passages.docid: 13717
negative_passages.text: Homomorphisms from $S_4$ to $\mathbb Z_2$
negative_passages.docid: 147968
negative_passages.text: Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
negative_passages.docid: 61709
negative_passages.text: Compute factor group $\dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle}$ - Fraleigh p. 147 Example 15.11
negative_passages.docid: 121034
negative_passages.text: Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
negative_passages.docid: 9140
negative_passages.text: Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$