Prove that $Sym(p)$ is generated by any transposition and any p-cycle
109440
How does $(12\dots n)$ and $(a\, b)$ generate $S_n$?
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
78263
Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$
7932
$(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula]
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
140199
Proof that disjoint cycles commute
132311
T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
43764
Prove $P_m X P_n$ is Hamiltonian if and only if at least one of $m,n$ is even
141802
Prove that free modules are projective
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
19026
What do all the $k$-cycles in $S_n$ generate?
52992
Proving that P/PJ is a projective right module over R/J
35472
Transitive subgroup of symmetric group $S_n$ containing an $(n-1)$-cycle and a transposition
40490
Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$