The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups

The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups

Suppose \(G\) is a finite group and \(H\) is a subgroup of \(G\). \(H\) is said to be \(s\)-permutably embedded in \(G\) if for each prime \(p\) dividing \(|H|\), a Sylow \(p\)-subgroup of \(H\) is also a Sylow \(p\)-subgroup of some \(s\)-permutable subgroup of \(G\); \(H\) is called  weakly \(s\)-...

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Збережено в:
Бібліографічні деталі
Дата:2018
Автор: Li, Changwen
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2018
Теми:
weakly s-permutably embedded subgroups; p-nilpotent; maximal subgroup; 2-maximal subgroup
20D10; 20D20
Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671
Теги: Додати тег
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Назва журналу:Algebra and Discrete Mathematics

Репозитарії

Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-671
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-6712018-04-04T09:28:39Z The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups Li, Changwen weakly s-permutably embedded subgroups; p-nilpotent; maximal subgroup; 2-maximal subgroup 20D10; 20D20 Suppose \(G\) is a finite group and \(H\) is a subgroup of \(G\). \(H\) is said to be \(s\)-permutably embedded in \(G\) if for each prime \(p\) dividing \(|H|\), a Sylow \(p\)-subgroup of \(H\) is also a Sylow \(p\)-subgroup of some \(s\)-permutable subgroup of \(G\); \(H\) is called  weakly \(s\)-permutably embedded in \(G\) if there are a subnormal subgroup  \(T\) of \(G\) and an \(s\)-permutably embedded subgroup \(H_{se}\) of \(G\) contained in \(H\) such that \(G=HT\) and \(H\cap T\leq H_{se}\). We investigate the influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671 Algebra and Discrete Mathematics; Vol 12, No 1 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671/205 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
collection OJS
language English
topic weakly s-permutably embedded subgroups; p-nilpotent; maximal subgroup; 2-maximal subgroup
20D10; 20D20
spellingShingle weakly s-permutably embedded subgroups; p-nilpotent; maximal subgroup; 2-maximal subgroup
20D10; 20D20
Li, Changwen
The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
topic_facet weakly s-permutably embedded subgroups; p-nilpotent; maximal subgroup; 2-maximal subgroup
20D10; 20D20
format Article
author Li, Changwen
author_facet Li, Changwen
author_sort Li, Changwen
title The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
title_short The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
title_full The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
title_fullStr The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
title_full_unstemmed The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
title_sort influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
description Suppose \(G\) is a finite group and \(H\) is a subgroup of \(G\). \(H\) is said to be \(s\)-permutably embedded in \(G\) if for each prime \(p\) dividing \(|H|\), a Sylow \(p\)-subgroup of \(H\) is also a Sylow \(p\)-subgroup of some \(s\)-permutable subgroup of \(G\); \(H\) is called  weakly \(s\)-permutably embedded in \(G\) if there are a subnormal subgroup  \(T\) of \(G\) and an \(s\)-permutably embedded subgroup \(H_{se}\) of \(G\) contained in \(H\) such that \(G=HT\) and \(H\cap T\leq H_{se}\). We investigate the influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671
work_keys_str_mv AT lichangwen theinfluenceofweaklyspermutablyembeddedsubgroupsonthepnilpotencyoffinitegroups
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first_indexed 2024-04-12T06:27:27Z
last_indexed 2024-04-12T06:27:27Z
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