How do I prove that the symmetric group $S_p$ where p is prime can be generated by any transposition and any p-cycle?
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.
41294
Permutation module of $S_n$
19026
What do all the $k$-cycles in $S_n$ generate?
53357
Cyclic Group Generators of Order $n$
96680
Generators of symmetric group $S_n$
122970
A question on $p$-groups, and order of its commutator subgroup.
79055
Orders of a symmetric group
122832
Proof for SSS Congruence?
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
78263
Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
147746
Characterisation of the squares of the symmetric group
104349
Proof by induction involving symmetric groups
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
126893
A group of order 2p (p prime) and other conditions - prove abelian.
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?