Show that $(\mathbb{Z}/2^n \mathbb{Z})^{\times}$ is not cyclic for any $n > 3.$
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
124438
Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
40131
If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
120183
Prove that $S_3\times\mathbb{Z}_2$ is isomorphic to $D_6$
144258
How to show a group is cyclic?
38507
Show that $\mathbb{Q}\times \mathbb{Q}$ is denumerable
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
25397
Prove $R \times R$ is NOT an integral domain
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.