A survey article on some subgroup embeddings and local properties for soluble PST-groups

Let \(G\) be a group and \(p\) a prime number. \(G\) is said to be a \(Y_p\textrm{-group}\) if whenever \(K\) is a \(p\)-subgroup of \(G\) then every subgroup of \(K\) is an S-permutable subgroup in \(N_G(K)\). The group \(G\) is a soluble PST-group if and only if \(G\) is a \(Y_p\textrm{-group}\) f...

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Дата:2017
Автор: Beidleman, James C.
Формат: Стаття
Мова:Англійська
Опубліковано: Lugansk National Taras Shevchenko University 2017
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Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/386
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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author Beidleman, James C.
author_facet Beidleman, James C.
author_sort Beidleman, James C.
baseUrl_str
collection OJS
datestamp_date 2017-07-02T21:58:40Z
description Let \(G\) be a group and \(p\) a prime number. \(G\) is said to be a \(Y_p\textrm{-group}\) if whenever \(K\) is a \(p\)-subgroup of \(G\) then every subgroup of \(K\) is an S-permutable subgroup in \(N_G(K)\). The group \(G\) is a soluble PST-group if and only if \(G\) is a \(Y_p\textrm{-group}\) for all primes \(p\).One of our purposes here is to define a number of local properties related to \(Y_p\) which lead to several new characterizations of soluble PST-groups. Another purpose is to define several embedding subgroup properties which yield some new classes of soluble PST-groups. Such properties include weakly S-permutable subgroup, weakly semipermutable subgroup, and weakly seminormal subgroup.
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spelling admjournalluguniveduua-article-3862017-07-02T21:58:40Z A survey article on some subgroup embeddings and local properties for soluble PST-groups Beidleman, James C. S-permutable subgroup, semipermutable subgroup, seminormal subgroup, PST-group 20D10, 20D20, 20D35 Let \(G\) be a group and \(p\) a prime number. \(G\) is said to be a \(Y_p\textrm{-group}\) if whenever \(K\) is a \(p\)-subgroup of \(G\) then every subgroup of \(K\) is an S-permutable subgroup in \(N_G(K)\). The group \(G\) is a soluble PST-group if and only if \(G\) is a \(Y_p\textrm{-group}\) for all primes \(p\).One of our purposes here is to define a number of local properties related to \(Y_p\) which lead to several new characterizations of soluble PST-groups. Another purpose is to define several embedding subgroup properties which yield some new classes of soluble PST-groups. Such properties include weakly S-permutable subgroup, weakly semipermutable subgroup, and weakly seminormal subgroup. Lugansk National Taras Shevchenko University NONE 2017-07-03 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/386 Algebra and Discrete Mathematics; Vol 23, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/386/pdf Copyright (c) 2017 Algebra and Discrete Mathematics
spellingShingle S-permutable subgroup
semipermutable subgroup
seminormal subgroup
PST-group
20D10
20D20
20D35
Beidleman, James C.
A survey article on some subgroup embeddings and local properties for soluble PST-groups
title A survey article on some subgroup embeddings and local properties for soluble PST-groups
title_full A survey article on some subgroup embeddings and local properties for soluble PST-groups
title_fullStr A survey article on some subgroup embeddings and local properties for soluble PST-groups
title_full_unstemmed A survey article on some subgroup embeddings and local properties for soluble PST-groups
title_short A survey article on some subgroup embeddings and local properties for soluble PST-groups
title_sort survey article on some subgroup embeddings and local properties for soluble pst-groups
topic S-permutable subgroup
semipermutable subgroup
seminormal subgroup
PST-group
20D10
20D20
20D35
topic_facet S-permutable subgroup
semipermutable subgroup
seminormal subgroup
PST-group
20D10
20D20
20D35
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/386
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