prove that $[G: xHx^{-1}]=[G:H]$
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
43645
Show that $G/H\cong S_3$
144732
If $[G:H]=n$, then $g^{n!}\in H$ for all $g\in G$.
27366
Prove that $g$ is tangent to the graph of $f$
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
147398
If every element of $H$ and $G/H$ is a square, then prove that so is every element of $G$.
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
136574
Show $g^{(n)}(0)=0$ for all $n$
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
110826
prove that : $ i = \sqrt {-1}\ $