To prove $o(HK) = o(H)o(K)/o(H\cap K)$
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
72551
Proof that $\rho = \pm1$ implies linear combination
44328
Prove that $\sum_{k=1} ^ n k^{-1} = \ln(n) + O(1)$
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
27901
Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
15259
Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
1251
If $[G:K]$ is finite, then $[H:H \cap K] = [G:K]$ iff $G = HK$ (Hungerford Proposition 4.8, Proof)
103441
Proving $(A\cup B)\cap(B\cup C)\cap(C\cup A)=(A\cap B)\cup (A\cap C)\cup (B\cap C)$?
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
28722
Prove that $H$ is a abelian subgroup of odd order
53475
Let $H$ have order $m$ and $K$ have order $n$, where $m$ and $n$ are relatively prime. Then $H \cap K=\{e\}$
145058
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $