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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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| 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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oai:ojs.admjournal.luguniv.edu.ua:article-8572018-03-21T12:28:31Z Groups whose non-normal subgroups have small commutator subgroup De Falco, M. de Giovanni, F. Musella, C. normal subgroup, commutator subgroup 20F24 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/857 Algebra and Discrete Mathematics; Vol 6, No 3 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/857/387 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-03-21T12:28:31Z |
| collection |
OJS |
| language |
English |
| topic |
normal subgroup commutator subgroup 20F24 |
| spellingShingle |
normal subgroup commutator subgroup 20F24 De Falco, M. de Giovanni, F. Musella, C. Groups whose non-normal subgroups have small commutator subgroup |
| topic_facet |
normal subgroup commutator subgroup 20F24 |
| format |
Article |
| author |
De Falco, M. de Giovanni, F. Musella, C. |
| author_facet |
De Falco, M. de Giovanni, F. Musella, C. |
| author_sort |
De Falco, M. |
| title |
Groups whose non-normal subgroups have small commutator subgroup |
| title_short |
Groups whose non-normal subgroups have small commutator subgroup |
| title_full |
Groups whose non-normal subgroups have small commutator subgroup |
| title_fullStr |
Groups whose non-normal subgroups have small commutator subgroup |
| title_full_unstemmed |
Groups whose non-normal subgroups have small commutator subgroup |
| title_sort |
groups whose non-normal subgroups have small commutator subgroup |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/857 |
| work_keys_str_mv |
AT defalcom groupswhosenonnormalsubgroupshavesmallcommutatorsubgroup AT degiovannif groupswhosenonnormalsubgroupshavesmallcommutatorsubgroup AT musellac groupswhosenonnormalsubgroupshavesmallcommutatorsubgroup |
| first_indexed |
2025-07-17T10:35:50Z |
| last_indexed |
2025-07-17T10:35:50Z |
| _version_ |
1837890064468672512 |