query: Let $\tau$ be a transposition (2-cycle) in $S_n$. Prove that for all permutations $\sigma$ in $S_n$, that $\sigma\tau\sigma^{-1}$ is a transposition.
positive_passages.docid: 13771
positive_passages.text: Why are two permutations conjugate iff they have the same cycle structure?
negative_passages.docid: 140199
negative_passages.text: Proof that disjoint cycles commute
negative_passages.docid: 128834
negative_passages.text: Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
negative_passages.docid: 100987
negative_passages.text: Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
negative_passages.docid: 144065
negative_passages.text: Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
negative_passages.docid: 14861
negative_passages.text: If $\sigma\in S_n$ is of length $n$, then $\sigma$ generates its centralizer
negative_passages.docid: 151520
negative_passages.text: About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
negative_passages.docid: 122504
negative_passages.text: Factorisations of permutations
negative_passages.docid: 57221
negative_passages.text: counting the number of elements in a conjugacy class of $S_n$
negative_passages.docid: 149801
negative_passages.text: prove that $TS = ST$
negative_passages.docid: 9140
negative_passages.text: Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
negative_passages.docid: 27985
negative_passages.text: If $\tau_1, \tau_2,\tau_3$ then which are correct?
negative_passages.docid: 27610
negative_passages.text: Given the permutation $\sigma=\left(\begin{array}{ccccc} 1&2&3&4&5\\ 3&1&2&5&4 \end{array}\right)$
negative_passages.docid: 128966
negative_passages.text: Explicit bijection between $\Bbb R$ and permutations of $\Bbb N$
negative_passages.docid: 149423
negative_passages.text: (combinatorics) prove that on average, n-permutations have Hn cycles without mathematical induction.
negative_passages.docid: 19026
negative_passages.text: What do all the $k$-cycles in $S_n$ generate?
negative_passages.docid: 135808
negative_passages.text: Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$