Prove the alternating group is generated by the set of 3-cycles.
58108
The alternating group is generated by three-cycles
149423
(combinatorics) prove that on average, n-permutations have Hn cycles without mathematical induction.
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
19026
What do all the $k$-cycles in $S_n$ generate?
84501
Proof involving Cyclic group, generator and GCD
49257
How to show that Klein four-group is a normal subgroup of the alternating group $A_4$
96680
Generators of symmetric group $S_n$
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
114752
Number of permutations of a specific cycle decomposition
100987
Let f be an r-cycle in $S_n$. Given any $h \in S_n$, show that $hfh^{-1} = (h(x_1), h(x_2), \dots, h(x_r))$
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
149609
Conditions on cycle types for permutations to generate $S_n$
97865
On Conjugacy Classes of Alternating Group $A_n$
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
131137
If ${\lvert{E(G)}\rvert}>{\lvert{V(G)}\rvert}+3$, graph $G$ has at least two disjoint cycles.
96123
Element of maximal order in alternating group $A_{10}$: how to prove this is it?
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.