Proof: $\mathbb{Z}_2 \oplus \mathbb{Z}_6 \not \cong \mathbb{Z}_{12}$
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
3317
Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
13317
show that $a^{12} \equiv 1 \mod 32760$ for each $a \in \mathbb{Z}$ such that $\text{gcd}(a, 32760) = 1$
15210
Group of order 6 proof
102429
There are 2 groups of order 6 (up to isomorphism)
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
11665
Show that $D_{12}$ is isomorphic to $D_6\times C_2$
52642
Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
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 $\mathbb Z [x]$
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
149030
Nonisomorphic groups of order 12.
57434
$SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong A_4$
88304
Center of $D_6$ is $\mathbb{Z}_2$
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.