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 is bounded in terms of k. We prove this conjecture for solvable groups.
Funding source: Ministerio de Ciencia e Innovación
Award Identifier / Grant number: PID2019-103854GB-I00
Funding source: Generalitat Valenciana
Award Identifier / Grant number: AICO/2020/298
Funding statement: Research supported by Ministerio de Ciencia e Innovación (Grant PID2019-103854GB-I00 funded by MCIN/AEI/10.13039/501100011033) and Generalitat Valenciana AICO/2020/298.
I thank the referee for his/her careful reading of the paper and helpful comments.
 F. Alizadeh, H. Behravesh, M. Ghaffarzadeh, M. Ghasemi and S. Hekmatara, Groups with few codegrees of irreducible characters, Comm. Algebra 47 (2019), no. 3, 1147–1152. 10.1080/00927872.2018.1501572Search in Google Scholar
 J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups, Clarendon Press, Oxford, 1985. Search in Google Scholar
 G. Malle and A. Moretó, A dual version of Huppert’s ρ-σ conjecture, Int. Math. Res. Not. IMRN 2007 (2007), no. 22, Article ID rnm 104. Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston