Chang-Guo Shao

Finite groups with conjugacy classes of size $2p^n$

We extend Burnside's $p^a$-Theorem on conjugacy classes of prime-power size by proving that no non-abelian finite simple group possesses a conjugacy class of size $2p^n$ for any prime $p$ and $n\geq 0$. Based on this, we partially extend a well-known result of L. Kazarin by showing that, given a finite group $G$, the s...