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 (Unpublished)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)|
|Uncontrolled Keywords:||Conjugacy classes; linear PC-groups; linear CC-groups; PChypercentral series; CC-hypercentral series MSC 2000 : 20C07; 20D10; 20F24.|
|Date Deposited:||18 Mar 2008|
|Last Modified:||30 Apr 2014 19:25|
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.
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