Let G be a finite group. Prove that elements in the same conjugacy class have conjugate centralizers. If cl,c2,..., ch are the orders of the centralizers of elements from the distinct conjugacy classes, prove that l/cx + l/c2 + ... + l/ch= 1. Deduce that there exist only finitely many finite groups with given class number h. Find all finite groups with class number 3 or less
