If $G \times G \cong H \times H$ must $G \cong H$?
40094
Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
35188
Counterexample: $G \times K \cong H \times K \implies G \cong H$
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
114394
Determine whether $\mathbb{Z}\times \mathbb{Z}$ and $\mathbb{Z}\times \mathbb{Z}\times \mathbb{Z}$ are isomorphic groups or not.
98542
Prove that $H$ is a subgroup of an abelian group $G$
135701
An example of a group such that $G \cong G \times G$
35626
Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
43645
Show that $G/H\cong S_3$
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
154398
Show that H is a subgroup of G
146760
Prove that H is a subgroup of G