Why is $(\mathbb{Z}\oplus\mathbb{Z})/\langle(3,6)\rangle$ not isomorphic to $\mathbb{Z}$?
124438
Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
89215
How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
87160
Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
30172
Why is the order of $\mathbb{Z}[i]/\langle 3+i\rangle$ equal to 10?
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
3161
Galois group of $x^6 + 3$ isomorphic to a copy of $S_3$ inside $S_6$
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
61709
Compute factor group $\dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle}$ - Fraleigh p. 147 Example 15.11
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
120183
Prove that $S_3\times\mathbb{Z}_2$ is isomorphic to $D_6$
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group