Showing that $G$ is isomorphic to $\{1,-1\}\times \mathbb{R}$
135855
Prove the group of all real translations and all glide reflections with axis$R$ is isomorphic to $\{1,-1\}\times \mathbb R$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
137949
If the quotient group $G/N$ be isomorphic to $G_2$, is $G$ isomorphic to $G_1\times G_2$ where $N$ is isomorphic to $G_1$?
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
154754
Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
57816
$(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$
46116
Proof of the First Isomorphism Theorem for Groups
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
22604
Can $R \times R$ be isomorphic to $R$ as rings?
81238
Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
36137
Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$