Showing that $\lvert H K\rvert = \frac{| H\| K|}{ |H\cap K|}$
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
28108
Proving the kernel is a normal subgroup.
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
1932
How to show this equality of $\rho(X,Y)$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
151621
$G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
71708
Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
71187
How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$?
51898
Show that $\operatorname{Hom}_{R} (R,M) \cong M$
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
60777
Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$