Understanding why the hint will prove that $A_{5}$ is generated by $3$-cycles.
31347
$A_n$ is generated by 3-cycles given $n\geq 3$. Is this proof correct?
40287
Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian
75461
If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
126590
Why is the multiplicative group of a finite field cyclic?
103146
Proof that the Rubik’s Cube group is 2-generated
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
127978
Another point of view that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is cyclic.
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
114752
Number of permutations of a specific cycle decomposition
158074
Cyclic group $G$ with generator $ab$.
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
66708
Elementary isomorphism between $\operatorname{PSL}(2,5)$ and $A_5$
134687
Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
3439
Other proofs that subgroups of $A_5$ have order at most 12
71451
A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
107163
Proof that $S_3$ isomorphic to $D_3$