Show that if $\sigma=(a_1,a_2,\dots,a_m)$ and $\tau$ is any element of $S_n$, then $\tau\sigma\tau^{-1}=(\tau a_1,\tau a_2,\dots,\tau a_m)$
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
151520
About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
41709
Show that the symmetric group $S_p = $, where $\sigma$ is any transposition and $\tau$ is any p- cycle and p is a prime number.
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
145352
How to prove $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group
151805
Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$
7530
Why this $\sigma \pi \sigma^{-1}$ keeps appearing in my group theory book? (cycle decomposition)
52483
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
64118
Number of elements in a finite $\sigma$-algebra
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
149801
prove that $TS = ST$
45939
For which $n≥2$ does there exist $\sigma\in A_n$ with $|\sigma| > n$
27985
If $\tau_1, \tau_2,\tau_3$ then which are correct?