Prove $N_1N_2/(N_1\cap N_2)\cong (N_1N_2/N_1) \times (N_1N_2/N_2)$, where $N_1, N_2$ are normal subgroups of $G$
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
89215
How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
75068
subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
107687
How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?
34567
If $G_1$ and $G_2$ are finite group and $H\leq G_1\times G_2$ then $H=P_1\times P_2$ with $P_i\leq G_i$?
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
51747
Showing that the intersection of all subgroups of order $n$ is normal
98284
show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
78564
Prove: $D_{8n} \not\cong D_{4n} \times Z_2$.
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
85129
If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?
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
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$