Given the group $(\mathbb Z,+)$,then find $n\mathbb Z \cap m\mathbb Z$ for arbitrary integers $n,m$
121280
Proving that $a \mathbb{Z} \cap b\mathbb{Z} = \operatorname{lcm}(a,b)\mathbb Z$
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
93703
Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
77957
How is $\mathbb N$ actually defined?
114262
Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
5906
All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
123482
How to compute $\mathbb{Z}_n^*$, the unit group of the integers modulo $n$?
5699
The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
52483
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
130826
Computing class group of $\mathbb Q(\sqrt{6})$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
102112
Idempotents in $\mathbb Z_n$
129239
Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity