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 |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/629 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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. |
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