Suppose $N \cap K = \{e_G\}$. Prove that for all $a \in N$ and $b \in K, ab = ba.$
39165
Suppose $G$ is a group and $H,K \trianglelefteq G$. If $H \cap K =1$ the $hk=kh$ for all $k \in K, h \in H$?
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
114599
$A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
49143
Showing $A \subset B \iff A\cap B=A$
1251
If $[G:K]$ is finite, then $[H:H \cap K] = [G:K]$ iff $G = HK$ (Hungerford Proposition 4.8, Proof)
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
3301
If $AB = I$ then $BA = I$
148108
Let $L=\operatorname{lcm}(o(a), o(b))$ and prove that $(ab)^L =e$.
60777
Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
53475
Let $H$ have order $m$ and $K$ have order $n$, where $m$ and $n$ are relatively prime. Then $H \cap K=\{e\}$
84422
$AB=BA$, $AC=CA$ we need to show $BC=CB$