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Algebra and Discrete Mathematics, 2009, Issue 4, Pages 135–157 (Mi adm148)  
This article is cited in 3 scientific papers (total in 3 papers)

SURVEY ARTICLE

Groups with small cocentralizers

Javier Otala, Nikolaj N.Semkob

a Departamento de Matemáticas — IUMA, Universidad de Zaragoza, Pedro Cerbuna 12. 50009 Zaragoza, SPAIN
b Department of Mathematics, National State Tax Service Academy of Ukraine, 09200 Irpen, UKRAINE.
Full-text PDF (315 kB) Citations (3)
Abstract: Let $G$ be a group. If $S\subseteq G$ is a $G$–invariant subset of $G$, the factor-group $G/C_G(S)$ is called the cocentralizer of $S$ in $G$. In this survey-paper we review some results dealing with the influence of several cocentralizers on the structure of the group, a direction of research to which Leonid A. Kurdachenko was an active contributor, as well as many mathematicians all around the world.
Keywords: Cocentralizer in a group. Groups with prescribed conjugacy classes: $FC$–groups. $CC$–groups. $PC$–groups. $MC$–groups.
Received: 07.07.2009
Revised: 07.07.2009
Bibliographic databases:
Document Type: Article
MSC: 20F24, 20F17
Language: English
Citation: Javier Otal, Nikolaj N.Semko, “Groups with small cocentralizers”, Algebra Discrete Math., 2009, no. 4, 135–157
Citation in format AMSBIB
\Bibitem{OtaSem09}
\by Javier~Otal, Nikolaj~N.Semko
\paper Groups with small cocentralizers
\jour Algebra Discrete Math.
\yr 2009
\issue 4
\pages 135--157
\mathnet{http://mi.mathnet.ru/adm148}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2681487}
\zmath{https://zbmath.org/?q=an:1199.20067}
Linking options:
  • https://www.mathnet.ru/eng/adm148
  • https://www.mathnet.ru/eng/adm/y2009/i4/p135
    • This publication is cited in the following 3 articles:
    1. Bouchelaghem M., Trabelsi N., “Groups Whose Proper Subgroups of Infinite Rank Have Minimax Conjugacy Classes”, J. Algebra. Appl., 16:1 (2017), 1750003  crossref  mathscinet  zmath  isi  scopus
    2. Kurdachenko L.A., Munoz-Escolano J.M., Otal J., “An Extension of a Theorem by B.H. Neumann on Groups with Boundedly Finite Conjugacy Classes”, Milan J. Math., 80:1 (2012), 227–241  crossref  mathscinet  zmath  isi  elib  scopus
    3. M. R. Dixon, V. V. Kirichenko, L. A. Kurdachenko, J. Otal, N. N. Semko, L. A. Shemetkov, I. Ya. Subbotin, “S. N. Chernikov and the development of infinite group theory”, Algebra Discrete Math., 13:2 (2012), 169–208  mathnet  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Algebra and Discrete Mathematics
    Statistics & downloads:
    Abstract page:214
    Full-text PDF :91
    References:5
    First page:1
     
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