A note on an extension of Shidov's theorem and Shlyk's theorem

Let $G$ be a non-solvable group and $p$ any fixed prime divisor of $|G|$. We prove that the intersection of all non-nilpotent maximal subgroups of $G$ of order divisible by $p$ containing the normalizer of some Sylow subgroup is $p$-closed, which provides a further generalization of Shidov's theorem and Shlyk's theorem.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.02608
Primary Topic
Finite Group Theory Research
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

A note on an extension of Shidov's theorem and Shlyk's theorem

Jiangtao Shi, Fanghua Li
arXiv (Cornell University)
Finite Group Theory Research
preprint

A note on an extension of Shidov's theorem and Shlyk's theorem

Jiangtao Shi, Fanghua Li
preprint en

Abstract

Let $G$ be a non-solvable group and $p$ any fixed prime divisor of $|G|$. We prove that the intersection of all non-nilpotent maximal subgroups of $G$ of order divisible by $p$ containing the normalizer of some Sylow subgroup is $p$-closed, which provides a further generalization of Shidov's theorem and Shlyk's theorem.

arXiv (Cornell University)
Finite Group Theory Research
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon
A note on an extension of Shidov's theorem and Shlyk's theorem — Jiangtao Shi, Fanghua Li · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS