If $H$ and $K$ are normal subgroups with $H\cap K=\{e\}$, then $xy=yx$ for $x\in H, y\in K$.
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
51359
Prove that every subgroup of an abelian group is a normal subgroup.
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
54911
The preimage of a normal subgroup under a group homomorphism is normal
98542
Prove that $H$ is a subgroup of an abelian group $G$
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
23533
All subgroups normal $\implies$ abelian group
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
139096
$|AxA|$ is a constant implies normal subgroup
44165
the image of normal subgroups
9110
Let G be a group such that $(xy)^2 = (yx)^2$ for all x, y ∈ G. Show that $xy^2 = y^2x$ for all x, y ∈ G.
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$