$H \cong K \times H$ implies $K$ is trivial?
58033
$G\times H\cong G$ with $H$ non-trivial
110635
Proving $\mathbb{N}^k$ is countable
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
128652
Subgroups of $\mathbb Z \times(\mathbb Z/n\mathbb Z)$
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
133238
Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
142851
Every group homomorphism from $(\mathbb{Q}, +)$ to $(\mathbb{Q}, \times)$ is the trivial map.
89659
$H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
146952
When can I say that $\cup H_i$ is a group?
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
133664
When the automorphism group is trivial......
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
15276
$G \times H \cong G \times K$ , then $ K \cong H$
43645
Show that $G/H\cong S_3$
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$