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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2010, том 9, выпуск 2, страницы 39–49 (Mi adm26)

Эта публикация цитируется 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.

MSC: 20D25, 20E45

Поступила в редакцию: 06.03.2009
Исправленный вариант: 05.11.2010

Язык публикации: английский



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