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Element orders and codegrees of characters in non-solvable groups.
- Source :
-
Journal of Algebra . Apr2024, Vol. 644, p428-441. 14p. - Publication Year :
- 2024
-
Abstract
- Given a finite group G and an irreducible complex character χ of G , the codegree of χ is defined as the integer cod (χ) = | G : ker (χ) | / χ (1). It was conjectured by G. Qian in [16] that, for every element g of G , there exists an irreducible character χ of G such that cod (χ) is a multiple of the order of g ; the conjecture has been verified under the assumption that G is solvable ([16]) or almost-simple ([13]). In this paper, we prove that Qian's conjecture is true for every finite group whose Fitting subgroup is trivial, and we show that the analysis of the full conjecture can be reduced to groups having a solvable socle. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SOLVABLE groups
*FINITE groups
*LOGICAL prediction
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 644
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 175412393
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2024.01.011