For groups, does $G \times G \cong H\times H$ imply $G \cong H$?
40094
Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
151130
When is the product of $n$ subgroups a subgroup?
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
103216
The set $\{g^2 | g \in G\}$ in a group $G$
4156
What is $\Bbb R^{\times}$? [unit group, ring to "times" power]
117538
What is the interpretation of $a \equiv b$ mod $H$ in group theory?
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 $P_i\leq G_i$?
146952
When can I say that $\cup H_i$ is a group?
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
61379
Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.
154398
Show that H is a subgroup of G
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...