Let $A$, $B$ be normal subgroups and $A\cap B=\{e\}$. Prove that $ab=ba$ for all $a\in A$, $b\in B$
3456
Commutator of two normal subgroups with trivial intersections
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
154878
Prove that $H$ is a normal subgroup in the finite group $G=\langle S\rangle $ iff $sHs^{-1}$ $\subseteq H$ for all $s\in S$.
10107
Prove $A\cup (A\cap B) = A$
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
28108
Proving the kernel is a normal subgroup.
1220
Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
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