This conjecture in "Unsolved problems in group theory" No.18: 9.24:


Conjecture: every finite simple non-abelian group $G$ can be represented in the form $G=CC$, where $C$ is some conjugacy class of $G$.


I want to prove this conjecture is right for simple group $A\_n$ in $S\_n$ ($n>4$), but I have no idea how to deal with it. I hope someone could give me some advice, or some old results about this. 



On J.G.Thompson's conjecture about conjugacy classes of finite simple groups
This was proved in this paper:



```
MR0183763 (32 #1241) Reviewed 
Xu Cheng-hao
The commutators of the alternating group. 
Sci. Sinica 14 1965 339–342. 
20.20 

```

My institution does not have an electronic copy, so there you are on your own.


