Groups with many generalized \(FC\)-subgroup
Let \(FC^0\) be the class of all finite groups, and for each non-negative integer \(m\) define by induction the group class \(FC^{m+1}\) consisting of all groups \(G\) such that the factor group \(G/C_G(x^G)\) has the property \(FC^m\) for all elements \(x\) of \(G\). Clearly, \(FC^1\) is the class...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/802 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | Let \(FC^0\) be the class of all finite groups, and for each non-negative integer \(m\) define by induction the group class \(FC^{m+1}\) consisting of all groups \(G\) such that the factor group \(G/C_G(x^G)\) has the property \(FC^m\) for all elements \(x\) of \(G\). Clearly, \(FC^1\) is the class of \(FC\)-groups and every nilpotent group with class at most \(m\) belongs to \(FC^m\). The class of \(FC^m\)-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-\(FC^m\)-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property \(FC^m\)) is investigated. |
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