Show that if f(n) is O(g(n) and d(n) is O(h(n)), then f(n) + d(n) is O(g(n) + h(n))
34713
Suppose $f(n)$ is $O(g(n))$ and $d(n)$ is $O(e(n))$. How do i use Big O to show that $f (n)$ + $d(n)$ is $O(g(n) + e(n))$?
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
98570
Prove whether $f(n)$ is $O$, $o$, $\Omega$, $\omega$ or $\Theta$ of $g(n)$. $f(n) = n + (\log n)^{2}$, $g(n) = n + \log(n^{2})$.
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
146760
Prove that H is a subgroup of G
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
15089
Big-O: If $f(n)=O(g(n))$, prove $2^{f(n)}=O(2^{(g(n)})$
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
104855
Prove that $N \subset Z(G)$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
76292
Showing that $f$ is identically $0$ on $\mathbb{D}$
121880
How to show that $|D_{2n}| = 2n$ via the presentation?
91980
Prove that f is one-to-one on D
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian