Camina groups with few conjugacy classes
Let \(G\) be a finite group having a proper normal subgroup \(K\) such that the conjugacy classes outside \(K\) coincide with the cosets of \(K\). The subgroup \(K\) turns out to be the derived subgroup of \(G\), so the group \(G\) is either abelian or Camina. Hence, we propose to classify Camina gr...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| 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/629 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543157380972544 |
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| author | Cangelmi, Leonardo Muktibodh, Arun S. |
| author_facet | Cangelmi, Leonardo Muktibodh, Arun S. |
| author_sort | Cangelmi, Leonardo |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:11:25Z |
| description | Let \(G\) be a finite group having a proper normal subgroup \(K\) such that the conjugacy classes outside \(K\) coincide with the cosets of \(K\). The subgroup \(K\) turns out to be the derived subgroup of \(G\), so the group \(G\) is either abelian or Camina. Hence, we propose to classify Camina groups according to the number of conjugacy classes contained in the derived subgroup. We give the complete characterization of Camina groups when the derived subgroup is made up of two or three conjugacy classes, showing that such groups are all Frobenius or extra-special. |
| first_indexed | 2026-02-08T07:57:57Z |
| format | Article |
| id | admjournalluguniveduua-article-629 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:57Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6292018-04-04T09:11:25Z Camina groups with few conjugacy classes Cangelmi, Leonardo Muktibodh, Arun S. Camina groups; Frobenius groups; Conjugacy classes 20D25; 20E45 Let \(G\) be a finite group having a proper normal subgroup \(K\) such that the conjugacy classes outside \(K\) coincide with the cosets of \(K\). The subgroup \(K\) turns out to be the derived subgroup of \(G\), so the group \(G\) is either abelian or Camina. Hence, we propose to classify Camina groups according to the number of conjugacy classes contained in the derived subgroup. We give the complete characterization of Camina groups when the derived subgroup is made up of two or three conjugacy classes, showing that such groups are all Frobenius or extra-special. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/629 Algebra and Discrete Mathematics; Vol 9, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/629/163 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Camina groups Frobenius groups Conjugacy classes 20D25 20E45 Cangelmi, Leonardo Muktibodh, Arun S. Camina groups with few conjugacy classes |
| title | Camina groups with few conjugacy classes |
| title_full | Camina groups with few conjugacy classes |
| title_fullStr | Camina groups with few conjugacy classes |
| title_full_unstemmed | Camina groups with few conjugacy classes |
| title_short | Camina groups with few conjugacy classes |
| title_sort | camina groups with few conjugacy classes |
| topic | Camina groups Frobenius groups Conjugacy classes 20D25 20E45 |
| topic_facet | Camina groups Frobenius groups Conjugacy classes 20D25 20E45 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/629 |
| work_keys_str_mv | AT cangelmileonardo caminagroupswithfewconjugacyclasses AT muktibodharuns caminagroupswithfewconjugacyclasses |