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 |
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| Автор: | |
| 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| _version_ | 1856543351077076992 |
|---|---|
| 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. |
| first_indexed | 2026-02-08T07:57:54Z |
| format | Article |
| id | admjournalluguniveduua-article-386 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:54Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| 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 |
| work_keys_str_mv | AT beidlemanjamesc asurveyarticleonsomesubgroupembeddingsandlocalpropertiesforsolublepstgroups AT beidlemanjamesc surveyarticleonsomesubgroupembeddingsandlocalpropertiesforsolublepstgroups |