A dual version of Huppert's rho-sigma conjecture for character codegrees

DOI10.1515/FORUM-2021-0257arXiv2110.02654WikidataQ113741111 ScholiaQ113741111MaRDI QIDQ6379535

Publication date: 6 October 2021

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 |

is bounded in terms of

k

. We prove this conjecture for solvable groups.

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

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