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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| Date: | 2017 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2017
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/386 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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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