PreprintCC BY 4.0arXiv
A note on an extension of Shidov's theorem and Shlyk's theorem
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.
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BibTeX
@misc{shi2026note,
title = {{A note on an extension of Shidov's theorem and Shlyk's theorem}},
author = {Jiangtao Shi and Fanghua Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02608},
eprint = {2611.02608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02608},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A note on an extension of Shidov's theorem and Shlyk's theorem
AU - Jiangtao Shi
AU - Fanghua Li
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02608
UR - https://arxiv.org/abs/2611.02608
AB - 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.
ER -