Proving that $\mathbb{Z}_{n}$ is cyclic
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
143069
What are the direct summands in $\mathbb{Z}^n$?
112933
Show that $Z\times Z$ is not cyclic...
102112
Idempotents in $\mathbb Z_n$
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
16559
Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
13734
Show that every group of prime order is cyclic
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
17239
Find all ideals of ${\mathbb{Z}_n}$
5906
All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $