A Note on Average Codegrees of All Proper Subgroups of Finite Groups

Let G be a finite group and let T( G ) be the sum of codegrees of complex irreducible characters of a group G . Say f( G )= T( G ) | G | . We prove that a finite group G such that for all proper subgroup H , 1.1f( H )1.3 , is solvable.

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Publication Details

Journal
Applied Mathematics
Published
2025-01-01
DOI
https://doi.org/10.4236/am.2025.164018
Primary Topic
Finite Group Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

A Note on Average Codegrees of All Proper Subgroups of Finite Groups

Shitian Liu, Wei Xie
Applied Mathematics
Finite Group Theory Research
article

A Note on Average Codegrees of All Proper Subgroups of Finite Groups

Shitian Liu, Wei Xie
article en

Abstract

Let G be a finite group and let T( G ) be the sum of codegrees of complex irreducible characters of a group G . Say f( G )= T( G ) | G | . We prove that a finite group G such that for all proper subgroup H , 1.1f( H )1.3 , is solvable.

Applied MathematicsVol. 16(04)
Sichuan University of Arts and Science (CN)
National Natural Science Foundation of China, Sichuan University
Reduced inequalities
Openalex Percentile: Top 88%
Finite Group Theory Research
DOIOpen Access PDFOpenAlex
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A Note on Average Codegrees of All Proper Subgroups of Finite Groups — Shitian Liu, Wei Xie · Applied Mathematics (2025) | TGRS Research Map | TGRS