Symmetric groups and conjugacy classes

Edith Adan-Bante, Helena Verrill

Let S_n be the symmetric group on n-letters. Fix n>5. Given any nontrivial $\alpha ,\beta \in S_n$, we prove that the product ${\alpha }^{S_n}{\beta }^{S_n}$ of the conjugacy classes ${\alpha }^{S_n}$ and ${\beta }^{S_n}$…