Prove $|G_1| \cdot |G_2| = |G_1G_2| \cdot |G_1 \cap G_2|$.
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
133915
In which case $M_1 \times N \cong M_2 \times N \Rightarrow M_1 \cong M_2$ is true?
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
147253
Prove for any $K \leq G$, either $K \leq N$ or $KN=G$ and $[K:K \cap N]=p$ where N is normal in G and $[G:N]=p$
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
52095
Prove either $G=ST$ or |$G|\geq|S|+|T|$
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
111515
Proving that $-a=(-1)\cdot a$
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
24951
Suppose $f_1 \in \Theta(g_1) \land f_2 \in \Theta(g_2)$. Prove $f_1 + f_2 \in \Theta(\max\{g_1, g_2\})$.
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
132487
Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$
62455
Prove Equivalence Relation in G
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$