Can we show that $\mathbb{Q}^c \cong \mathbb{R}$?
117366
Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?
5996
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
76100
Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
105666
What's an easy way to show that $GL(n,\mathbb C)$ is connected?
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
155750
Why does $\mathbb{C}$ have transcendence degree $\mathfrak{c}$ over $\mathbb{Q}$?
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
76048
Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$?
133238
Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
9129
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
152297
Understanding quotients of $\mathbb{Q}[x]$
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension