Minimal number of 3-cycles that generates $A_n$

Question

It is a well known fact that $A_n$ is generated by 3-cycles.

If we denote by $N$ the minimal number of 3-cycles needed to generate $A_n$, I'm looking for an estimate of such $N$ as function of $n$.

In particular my claim is that $N=O(n)$ but I don't know how to prove it.

Any help or reference is well accepted.

Answer 1

See Conrad's paper:

http://www.math.uconn.edu/~kconrad/blurbs/grouptheory/genset.pdf

Certainly, $A_n$ is generated by $3-$cycles. However, you may reduce this to precisely

$$\{(12i) \mid 1\leq i \leq n-2\},$$

which is minimal of length $n-2.$ This works for $n\geq 5.$