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Algebra Discrete Math., 2010, Volume 9, Issue 2, Pages 39–49 (Mi adm26)  

This article is cited in 2 scientific papers (total in 2 papers)

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

Abstract: 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.

Keywords: Camina groups; Frobenius groups; conjugacy classes.

Full text: PDF file (213 kB)

Bibliographic databases:
MSC: 20D25, 20E45
Received: 06.03.2009
Revised: 05.11.2010
Language:

Citation: Leonardo Cangelmi, Arun S. Muktibodh, “Camina groups with few conjugacy classes”, Algebra Discrete Math., 9:2 (2010), 39–49

Citation in format AMSBIB
\Bibitem{CanMuk10}
\by Leonardo Cangelmi, Arun S. Muktibodh
\paper Camina groups with few conjugacy classes
\jour Algebra Discrete Math.
\yr 2010
\vol 9
\issue 2
\pages 39--49
\mathnet{http://mi.mathnet.ru/adm26}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2808779}
\zmath{https://zbmath.org/?q=an:1209.20022}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Arora H., Karan R., “a Note on Autocamina Groups”, Note Mat., 35:2 (2015), 39–50  crossref  mathscinet  zmath  isi
    2. Sheikh-Mohseni S., Saeedi F., “Camina Lie Algebras”, Asian-Eur. J. Math., 11:5 (2018), 1850063  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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