Proof that $ (\mathbb{Z} \times \mathbb{Z},+) /\langle(2,3)\rangle $ is cyclic.
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
92517
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
126590
Why is the multiplicative group of a finite field cyclic?
2626
Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
89215
How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
94296
Classifying the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
45213
Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
13682
Is $\langle a,b \mid a^2b^2=1 \rangle$ a semidirect product of $\mathbb{Z}^2$ and $\mathbb{Z}_2$?
107716
Show that $G$ is cyclic
48452
Proof that $\gcd$ divides $\operatorname{lcm}$
61292
How to know which elements are in the Quotient Ring $\mathbb{Z}[x]/\langle x, 2\rangle$?
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$