Show that $\mathcal D_{12}\cong C_2\times \mathfrak S_3$
119793
Proving that $D_{12}\cong S_3 \times C_2$
14139
$(12)$ and $(123\dots n)$ are generators of $S_n$
147968
Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
121034
Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
9129
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
76100
Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
61709
Compute factor group $\dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle}$ - Fraleigh p. 147 Example 15.11
133612
How many isomorphisms are there from $\Bbb Z_{12}$ to $\Bbb Z_{4} \oplus \Bbb Z_{3}$?
98284
show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
137201
Classifying $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z} / \langle(3,3,3)\rangle$
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
83747
$2$ out of $3$ property of the unitary group
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
16172
My proof of $I \otimes N \cong IN$ is clearly wrong, but where have I gone wrong?
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$