Prime divisors and the number of conjugacy classes of finite groups

Abstract

AbstractWe prove that there exists a universal constant D such that if p is a prime divisor of the index of the Fitting subgroup of a finite group G, then the number of conjugacy classes of G is at least $Dp/\log_2p$ . We conjecture that we can take $D=1$ and prove that for solvable groups, we can take $D=1/3$ .