Groups whose non-normal subgroups have small commutator subgroup
The structure of groups whose non-normal subgroups have a finite commutator subgroup is investigated. In particular, it is proved that if \(k\) is a positive integer and \(G\) is a locally graded group in which every non-normal subgroup has finite commutator subgroup of order at most \(k\), then the...
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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/857 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | The structure of groups whose non-normal subgroups have a finite commutator subgroup is investigated. In particular, it is proved that if \(k\) is a positive integer and \(G\) is a locally graded group in which every non-normal subgroup has finite commutator subgroup of order at most \(k\), then the commutator subgroup of \(G\) is finite. Moreover, groups with finitely many normalizers of subgroups with large commutator subgroup are studied. |
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