A dual version of Huppert's ρ-σ conjecture for character codegrees

Abstract

Abstract We classify the finite groups with the property that any two different character codegrees are coprime. In general, we conjecture that if k is a positive integer such that for any prime p the number of character codegrees of a finite group G that are divisible by p is at most k, then the number of prime divisors of | G | {|G|} is bounded in terms of k. We prove this conjecture for solvable groups.