Products of three conjugacy classes in the alternating group

Daniele Dona

We prove that for $\delta$ small, $n$ large, and any three conjugacy classes $C_1,C_2,C_3$ of $G=\mathrm{Alt}(n)$ of size at least $|G{|}^{1-\delta }$ we have $C_1{C}_2{C}_3=G$. The res…