Invariant factors of $\mathbb Z_m\times\mathbb Z_n$
4648
Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
146978
Minimal and characteristic polynomial have same set of irreducible factors
120183
Prove that $S_3\times\mathbb{Z}_2$ is isomorphic to $D_6$
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
137186
Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).
13761
Automorphisms in $\mathbb{Z}_n$
94296
Classifying the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$
31391
bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$
149578
Subgroups of $(\mathbb Z_n,+)$
137201
Classifying $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z} / \langle(3,3,3)\rangle$
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
149783
$\mathbb Z\times\mathbb Z$ is principal but is not a PID
55432
Infinite distinct factorizations into irreducibles for an element
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
89415
Number of homomorphisms from $(\mathbb Q^+ , \,\cdot\,)$ to $(\mathbb Z_n , +)$