$G×G$ and $H×H$ being isomorphic implies $G $ and $H $ are isomorphic
123860
When are two direct products of groups isomorphic?
140962
Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
58707
Prove Quotient Group Isomorphism
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
15276
$G \times H \cong G \times K$ , then $ K \cong H$
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
107163
Proof that $S_3$ isomorphic to $D_3$
102371
Proving that two vector spaces of equal dimension are isomorphic
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
152603
Group isomorphic to its automorphism group
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
46863
Show that $g$ is injective
148881
Aut(GxH) isomorphic to Aut(G)xAut(H)