Show that $o(g_1\cdot g_2)=o(g_1)\cdot o(g_2)$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
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 $O(g(n) + e(n))$?
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
65744
How can I Prove that H=G or K=G
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
117815
Non-abelian group $G$ satisfying $(a \cdot b)^i=a^i \cdot b^i,$ for two consecutive integers.
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
129605
$ 2g(z)=g(\frac{z}{2}) + g(\frac{z+1}{2})$
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
82935
Prove that f∈Θ(g)if and only ifO(f) =O(g).
81116
$gh = hg, \ \gcd(|g|, |h|) = 1\Rightarrow|gh| = |g||h|\ \ (|a|$ = order of element $a)$
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$