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

Alexander Moretó ORCID logo
From the journal Forum Mathematicum


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| is bounded in terms of k. We prove this conjecture for solvable groups.

MSC 2010: 20C15

Communicated by Freydoon Shahidi

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.


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Received: 2021-10-05
Revised: 2021-12-09
Published Online: 2022-01-23
Published in Print: 2022-03-01

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