Kernels of minimal characters of solvable groups

Abstract Let G be a finite solvable group. We prove that if $\chi\in{{\operatorname{Irr}}}(G)$ has odd degree and $\chi(1)$ is the minimal degree of the nonlinear irreducible characters of G , then $G/\operatorname{Ker}\chi$ is nilpotent-by-abelian.

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Publication Details

Journal
Proceedings of the Edinburgh Mathematical Society
Published
2024-11-01
DOI
https://doi.org/10.1017/s0013091524000427
Primary Topic
Finite Group Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

Kernels of minimal characters of solvable groups

Alexander Moretó
Proceedings of the Edinburgh Mathematical Society
Finite Group Theory Research
article

Kernels of minimal characters of solvable groups

Alexander Moretó
article en

Abstract

Abstract Let G be a finite solvable group. We prove that if $\chi\in{{\operatorname{Irr}}}(G)$ has odd degree and $\chi(1)$ is the minimal degree of the nonlinear irreducible characters of G , then $G/\operatorname{Ker}\chi$ is nilpotent-by-abelian.

Proceedings of the Edinburgh Mathematical SocietyVol. 67(4)
Universitat de València (ES)
Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación
Reduced inequalities
Openalex Percentile: Top 64%
Finite Group Theory Research
DOIOpen Access PDFOpenAlex
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Kernels of minimal characters of solvable groups — Alexander Moretó · Proceedings of the Edinburgh Mathematical Society (2024) | TGRS Research Map | TGRS