On the partial $ \mathscr L $-$ Π$-property of subgroups of finite groups

Fuente: arXiv
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Auteurs principaux: Qiu, Zhengtian, Ballester-Bolinches, Adolfo
Format: Preprint
Publié: 2024
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author Qiu, Zhengtian
Ballester-Bolinches, Adolfo
author_facet Qiu, Zhengtian
Ballester-Bolinches, Adolfo
contents Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ \mathscr L $-$ Π$-property in $ G $ if $ H\unlhd G $, or if $ | G / K : \mathrm{N} _{G / K} (HK/K)| $ is a $ π(HK/K) $-number for any $ G $-chief factor of type $ H^{G}/K $ with $ H_{G}\leq K $. In this paper, we investigate the structure of finite groups under the assumption that some subgroups of prime power order satisfy the partial $ \mathscr L $-$ Π$-property.
format Preprint
id arxiv_https___arxiv_org_abs_2408_06348
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the partial $ \mathscr L $-$ Π$-property of subgroups of finite groups
Qiu, Zhengtian
Ballester-Bolinches, Adolfo
Group Theory
Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ \mathscr L $-$ Π$-property in $ G $ if $ H\unlhd G $, or if $ | G / K : \mathrm{N} _{G / K} (HK/K)| $ is a $ π(HK/K) $-number for any $ G $-chief factor of type $ H^{G}/K $ with $ H_{G}\leq K $. In this paper, we investigate the structure of finite groups under the assumption that some subgroups of prime power order satisfy the partial $ \mathscr L $-$ Π$-property.
title On the partial $ \mathscr L $-$ Π$-property of subgroups of finite groups
topic Group Theory
url https://arxiv.org/abs/2408.06348