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Russo, Francesco (2007) Generalized FC-groups in Finitary Groups. In: Group Theory Seminars in Michigan State University, 30 Ott 2007, East Lansing, USA. (Unpublished)

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Item Type: Conference or Workshop Item (Speech)
Title: Generalized FC-groups in Finitary Groups
Creators:
CreatorsEmail
Russo, Francescofrancesco.russo@dma.unina.it
Date: 30 October 2007
Date Type: Publication
Number of Pages: 31
Event Type: Workshop
Event Title: Group Theory Seminars in Michigan State University
Event Location: East Lansing, USA
Event Dates: 30 Ott 2007
Date: 30 October 2007
Number of Pages: 31
Uncontrolled Keywords: Conjugacy classes; linear PC-groups; linear CC-groups; PChypercentral series; CC-hypercentral series MSC 2000 : 20C07; 20D10; 20F24.
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MIUR S.S.D.: Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria
Area 01 - Scienze matematiche e informatiche > MAT/02 - Algebra
Date Deposited: 18 Mar 2008
A group $G$ is called $FC$-group if it is a group in which each element has finitely many conjugates. This condition is equivalent to require that $G/C_G(x^G)$ is a finite group for each element $x$ of $G$, where the symbol $x^G$ denotes the normal closure of the subgroup $\langle x \rangle$ in $G$. A group $G$ is called $CC$-group if $G/C_G(x^G)$ is a Chernikov group for each element $x$ of $G$. A group $G$ is called $PC$-group if $G/C_G(x^G)$ is a polycyclic-by-finite group for each element $x$ of $G$. $FC$-groups are subclasses of the classes of $CC$-groups and $PC$-groups. Here we investigate finitary linear groups which have generalized series of $CC$-groups and $PC$-groups.