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Algebra and Discrete Mathematics, 2010, том 9, выпуск 2, страницы 39–49
(Mi adm26)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
RESEARCH ARTICLE
Camina groups with few conjugacy classes
Leonardo Cangelmia, Arun S. Muktibodhb a Dipartimento di Scienze, Università di Chieti-Pescara,
V. le Pindaro 42, 65127 Pescara, Italy
b Department of Mathematics, Mohota Science College, Umred Rd.
Nagpur-440009, India
Аннотация:
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.
Ключевые слова:
Camina groups; Frobenius groups; conjugacy classes.
Поступила в редакцию: 06.03.2009 Исправленный вариант: 05.11.2010
Образец цитирования:
Leonardo Cangelmi, Arun S. Muktibodh, “Camina groups with few conjugacy classes”, Algebra Discrete Math., 9:2 (2010), 39–49
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm26 https://www.mathnet.ru/rus/adm/v9/i2/p39
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