Counting subgroups of a finite group containing a prescribed subgroup

Let $R$ be a finite group, and let $T$ be a subgroup of $R$. We show that there are at most \[ 7.3722[R:T]^{\frac{\log_2[R:T]}{4}+1.8919} \] subgroups of $R$ containing $T$.

Publication Details

Journal
ArXiv.org
Published
2025-05-01
Primary Topic
Finite Group Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

Counting subgroups of a finite group containing a prescribed subgroup

ArXiv.org
Finite Group Theory Research
article

Counting subgroups of a finite group containing a prescribed subgroup

article en

Abstract

Let $R$ be a finite group, and let $T$ be a subgroup of $R$. We show that there are at most \[ 7.3722[R:T]^{\frac{\log_2[R:T]}{4}+1.8919} \] subgroups of $R$ containing $T$.

ArXiv.org
Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
Openalex Percentile: Top 45%
Finite Group Theory Research
Open Access PDFOpenAlex
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Counting subgroups of a finite group containing a prescribed subgroup · ArXiv.org (2025) | TGRS Research Map | TGRS